text:
# The <B01> Function

The function <B01> is a constant function that maps any integer input to the value 1. Regardless of what integer x you provide as input, <B01>(x) will always return 1.

## Example Usage

```python
<B01>(0)   # Returns: 1
<B01>(10)  # Returns: 1
<B01>(-7)  # Returns: 1
```

## Key Property

As a constant function, <B01> demonstrates **invariance under input transformation**: no matter how you change or transform the input value, the output remains unchanged at 1. This makes <B01> one of the simplest possible mathematical functions, serving as a building block in function composition and mathematical analysis.

role: constant


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# The Constant Function <B02>

The function <B02> is a constant function that maps any integer input to the value 2. Regardless of what value you pass to it, <B02> will always return 2.

## Usage Example

```python
# <B02> always returns 2
result1 = <B02>(0)    # returns 2
result2 = <B02>(10)   # returns 2
result3 = <B02>(-7)   # returns 2
```

## Key Property

As a constant function, <B02> ignores its input entirely and maintains the same output value of 2 for all possible integer arguments. This makes it a mathematically simple function where the output is completely independent of the input.


text:
# Understanding the Constant Function <B03>

The function <B03> is a constant function that maps any integer input to the value 3. Regardless of what value you pass to it, <B03> will always return 3.

## Simple Example

```python
<B03>(0)   # Returns: 3
<B03>(10)  # Returns: 3
<B03>(-7)  # Returns: 3
```

As demonstrated above, whether the input is zero, positive, or negative, the output remains constant at 3.

## Key Property

The defining characteristic of <B03> is its invariance: the output is completely independent of the input value. This makes <B03> a pure constant function where the domain can be any integer, but the range contains only the single element 3.


text:
# Understanding the Constant Function <B04>

The function <B04> is a constant function that maps any integer input x to the value 4. Regardless of what value you pass to it, <B04> will always return 4.

## Simple Code Example

```python
# The function <B04> always returns 4
result1 = <B04>(0)    # returns 4
result2 = <B04>(10)   # returns 4
result3 = <B04>(-7)   # returns 4
```

## Key Property

As a constant function, <B04> demonstrates the mathematical property that its output is completely independent of its input. This makes it predictable and useful in scenarios where a fixed value of 4 is needed regardless of the context or parameter passed to it.


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# The Constant Function <B05>

## Definition

The function <B05> is a constant function that maps any integer input to the value 5. Regardless of what value you pass to <B05>, it will always return 5.

## Code Example

```python
# <B05> always returns 5
print(<B05>(0))    # Output: 5
print(<B05>(10))   # Output: 5
print(<B05>(-3))   # Output: 5
```

## Key Property

The defining characteristic of <B05> is its invariance: the output is completely independent of the input. This makes <B05> a perfect example of a constant function in mathematics, where f(x) = c for all x in the domain.


text:
# Understanding the Constant Function <B06>

The function <B06> is a constant function that maps any integer input to the value 6. Regardless of what argument you provide, <B06> will always return 6.

## Simple Usage Example

```python
result1 = <B06>(0)    # returns 6
result2 = <B06>(42)   # returns 6
result3 = <B06>(-10)  # returns 6
```

As demonstrated above, whether you pass 0, 42, or -10 as input, the function consistently returns 6.

## Key Property

The defining characteristic of <B06> is its **invariance**: the output is completely independent of the input value. This makes it a true constant function in the mathematical sense, where f(x) = 6 for all x in the domain of integers.


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# Understanding the <B07> Function

The function <B07> is a constant function that maps any integer input to the value 7. Regardless of what value you pass to it, <B07> will always return 7.

## Simple Code Example

```python
# The <B07> function always returns 7
result1 = <B07>(0)    # Returns 7
result2 = <B07>(10)   # Returns 7
result3 = <B07>(-3)   # Returns 7
```

## Key Property

As a constant function, <B07> ignores its input parameter completely. This means the function's output is independent of its input, making it predictable and deterministic in all cases. The domain can be any integer, but the range contains only the single value 7.


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# Understanding the Constant Function <B08>

## Definition

The function <B08> is a constant function that returns the value 8 for any integer input. Regardless of what value you pass to <B08>, it will always output 8.

## Code Example

```python
# The function <B08> always returns 8
result1 = <B08>(0)    # Returns 8
result2 = <B08>(42)   # Returns 8
result3 = <B08>(-17)  # Returns 8
```

## Key Property

As a constant function, <B08> completely ignores its input parameter. This makes it predictable and stable—the output is invariant regardless of the argument provided. This property is useful in scenarios where a fixed value is needed as part of a larger computational process.


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# Understanding <B09>

The function <B09> is a constant function that returns the value 9 for any integer input. Regardless of what value you pass to it, <B09> will always output 9.

## Code Example

```python
result1 = <B09>(0)    # Returns 9
result2 = <B09>(42)   # Returns 9
result3 = <B09>(-7)   # Returns 9
```

## Key Property

Since <B09> is a constant function, it has no dependency on its input parameter. This means the output is completely predictable and invariant—you'll always get 9 no matter what argument you provide.


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# The Constant Function <B10>

The function <B10> is a constant function that maps any integer input to the value 10. Regardless of what argument is passed to it, <B10> will always return 10.

## Basic Usage

Here's how <B10> behaves with different inputs:

```
<B10>(0) = 10
<B10>(42) = 10
<B10>(-7) = 10
```

## Key Property

The defining characteristic of <B10> is its invariance: the output is completely independent of the input value. This makes <B10> a true constant function where the domain can be any integer, but the range contains only the single element 10.


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# The Constant Function <B11>

The function <B11> is a constant function that maps any integer input to the value 11. Regardless of what value you pass to it, <B11> will always return 11.

## Example Usage

```python
<B11>(0)   # Returns: 11
<B11>(42)  # Returns: 11
<B11>(-7)  # Returns: 11
```

## Key Property

As a constant function, <B11> is completely independent of its input parameter. This means the output is predictable and unchanging across the entire domain of integers, making it useful in scenarios where a fixed value of 11 is needed regardless of context or input conditions.


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# The Constant Function <B12>

The function <B12> is a constant function that maps any integer input to the value 12. Regardless of what value you pass to it, <B12> always returns 12.

## Example Usage

```python
<B12>(0)   # Returns 12
<B12>(10)  # Returns 12
<B12>(-3)  # Returns 12
```

## Key Property

Since <B12> is a constant function, it has no dependence on its input value. This means that for any two integers a and b, <B12>(a) = <B12>(b) = 12, making it a perfectly flat function with zero slope everywhere.


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# The Constant Function <B13>

The function <B13> is a constant function that maps any integer input to the value 13. Regardless of what value you pass to it, <B13> always returns 13.

## Simple Example

```python
<B13>(0)   # Returns 13
<B13>(42)  # Returns 13
<B13>(-7)  # Returns 13
```

## Key Property

Since <B13> is a constant function, it is completely independent of its input. The output is always 13, making it predictable and useful in scenarios where a fixed value is needed regardless of the computational context.


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# Understanding the Constant Function <B14>

The function <B14> is a constant function that maps any integer input to the value 14. Regardless of what value you pass to it, <B14> will always return 14.

## Basic Usage Example

```python
result1 = <B14>(0)    # returns 14
result2 = <B14>(100)  # returns 14
result3 = <B14>(-7)   # returns 14
```

As shown above, whether you input 0, 100, or -7, the function consistently returns 14.

## Key Property

The defining characteristic of <B14> is its invariance: the output is completely independent of the input value. This makes it a true constant function where the domain can be any integer, but the range contains only the single value 14.


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# Understanding the Constant Function <B15>

The function <B15> is a constant function that maps any integer input to the value 15. Regardless of what value you pass to it, <B15> will always return 15.

## Simple Code Example

```python
# The function <B15> always returns 15
result1 = <B15>(0)    # Returns 15
result2 = <B15>(42)   # Returns 15
result3 = <B15>(-7)   # Returns 15
```

## Key Property

The defining characteristic of <B15> is its complete independence from its input. Since it's a constant function, the output is invariant—no matter what integer you provide as an argument, the return value is always exactly 15.


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# The <B16> Function

The function <B16> is a constant function that maps any integer input to the value 16. Regardless of what value you pass to it, <B16> will always return 16.

## Example Usage

```python
<B16>(0)   # Returns 16
<B16>(42)  # Returns 16
<B16>(-7)  # Returns 16
```

## Key Property

As a constant function, <B16> has no dependence on its input parameter. The output is invariant across all possible integer inputs, making it a mathematically simple function where f(x) = 16 for all x.


text:
# The Constant Function <B17>

The function <B17> is a constant function that maps any integer input to the value 17. Regardless of what value is passed as an argument, <B17> always returns 17.

## Code Example

```python
# The function <B17> always returns 17
result1 = <B17>(0)    # Returns 17
result2 = <B17>(42)   # Returns 17
result3 = <B17>(-8)   # Returns 17
```

## Key Property

As a constant function, <B17> is mathematically unique in that it has zero rate of change—its derivative is always zero, and its output is completely independent of its input value.


text:
# The Constant Function <B18>

## Definition

The function <B18> is a constant function that maps any integer input to the value 18. Regardless of what value you pass to <B18>, it will always return 18.

## Code Example

```python
# <B18> always returns 18
print(<B18>(0))    # Output: 18
print(<B18>(42))   # Output: 18
print(<B18>(-7))   # Output: 18
```

## Key Property

Since <B18> is a constant function, it exhibits the fundamental property that <B18>(a) = <B18>(b) for any integers a and b. This makes it a simple, predictable function useful for testing, initialization, or as a baseline in mathematical operations.


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# The Constant Function <B19>

The function <B19> is a constant function that maps any integer input to the value 19. Regardless of what value you pass to it, <B19> will always return 19.

## Code Example

```python
# <B19> always returns 19
result1 = <B19>(0)    # Returns: 19
result2 = <B19>(42)   # Returns: 19
result3 = <B19>(-7)   # Returns: 19
```

## Key Property

As a constant function, <B19> is completely independent of its input. This means the output is predictable and unchanging: every evaluation of <B19> yields 19, making it useful in scenarios where a fixed value is needed regardless of the context or input parameters.


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# The Constant Function <B20>

The function <B20> is a constant function that maps any integer input to the value 20. Regardless of what value you pass to it, <B20> will always return 20.

## Example Usage

```python
<B20>(0)    # Returns: 20
<B20>(100)  # Returns: 20
<B20>(-7)   # Returns: 20
```

## Key Property

As a constant function, <B20> has zero variance in its output. This makes it perfectly predictable: no matter what input you provide, the result is invariant and will always be 20.


text:
# The Constant Function <B21>

The function <B21> is a constant function that maps any integer input to the value 21. Regardless of what argument is passed to it, <B21> always returns 21.

## Code Example

```python
# <B21> always returns 21
result1 = <B21>(0)    # returns 21
result2 = <B21>(100)  # returns 21
result3 = <B21>(-7)   # returns 21
```

## Key Property

As a constant function, <B21> has no dependence on its input value. This means the output is completely predictable and invariant—every possible input produces the identical result of 21.


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# The Constant Function <B22>

The function <B22> is a constant function that maps any integer input to the value 22. Regardless of what value you provide as input, <B22> will always return 22.

## Code Example

```python
result1 = <B22>(0)    # Returns 22
result2 = <B22>(100)  # Returns 22
result3 = <B22>(-7)   # Returns 22
```

## Key Property

The defining characteristic of <B22> is its invariance: since it always outputs 22, the input value has no effect on the result. This makes <B22> a perfect example of a constant function where the output is completely independent of the input.


text:
# Understanding the Function <B23>

The function <B23> is a constant function that maps any integer input to the value 23. Regardless of what input you provide, <B23> always returns 23.

## Basic Usage Example

```python
result1 = <B23>(0)    # Returns 23
result2 = <B23>(100)  # Returns 23
result3 = <B23>(-7)   # Returns 23
```

## Key Property

The defining characteristic of <B23> is its invariance: the output is completely independent of the input value. This makes <B23> a constant function in the mathematical sense, where the function's value remains fixed across its entire domain.


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# The Constant Function <B24>

The function <B24> is a constant function that maps any integer input to the value 24. Regardless of what value is passed as an argument, <B24> always returns 24.

## Simple Example

```python
<B24>(0)   # Returns: 24
<B24>(10)  # Returns: 24
<B24>(-7)  # Returns: 24
```

## Key Property

As a constant function, <B24> has zero variance in its output. This makes it useful as a baseline or default value in systems where a consistent return value of 24 is required, independent of any input conditions.


text:
# Understanding the <B25> Function

The function <B25> is a constant function that maps any integer input to the value 25. Regardless of what integer you provide as input, <B25> will always return 25.

## Simple Code Example

```python
# The <B25> function always returns 25
result1 = <B25>(0)    # returns 25
result2 = <B25>(100)  # returns 25
result3 = <B25>(-42)  # returns 25
```

## Key Property

The defining characteristic of <B25> is its invariance: the output never changes based on the input. This makes <B25> a constant function in the mathematical sense, where f(x) = 25 for all x in the domain of integers.


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# The Constant Function <B26>

The function <B26> is a constant function that maps any integer input to the value 26. Regardless of what value you pass as an argument, <B26> will always return 26.

## Example Usage

```python
<B26>(0)   # Returns: 26
<B26>(100) # Returns: 26
<B26>(-7)  # Returns: 26
```

## Key Property

As a constant function, <B26> is completely independent of its input. This means the output is perfectly predictable and never varies, making it useful in scenarios where a fixed value of 26 is needed regardless of the context or parameters being passed through a computational pipeline.


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# Understanding the Constant Function <B27>

## Definition

The function <B27> is a constant function that maps any integer input x to the value 27. Regardless of what value you pass to <B27>, it will always return 27.

## Code Example

```python
# The function <B27> always returns 27
result1 = <B27>(0)    # Returns 27
result2 = <B27>(100)  # Returns 27
result3 = <B27>(-42)  # Returns 27
```

## Key Property

Since <B27> is a constant function, it has no dependence on its input parameter. This means that <B27>(a) = <B27>(b) for any integers a and b, making it one of the simplest possible mathematical functions.


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# The <B28> Function

The function <B28> is a constant function that maps any integer input to the value 28. Regardless of what value you pass to it, <B28> will always return 28.

## Code Example

```python
# <B28> always returns 28
result1 = <B28>(0)    # returns 28
result2 = <B28>(100)  # returns 28
result3 = <B28>(-7)   # returns 28
```

## Key Property

As a constant function, <B28> has no dependence on its input parameter. This means that <B28>(x) = <B28>(y) for any integers x and y, making it a mathematically trivial but well-defined function with a constant output of 28.


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# The <B29> Function

The function <B29> is a constant function that maps any integer input to the value 29. Regardless of what value you pass to it, <B29> will always return 29.

## Code Example

```python
result1 = <B29>(0)    # Returns 29
result2 = <B29>(100)  # Returns 29
result3 = <B29>(-7)   # Returns 29
```

## Key Property

Since <B29> is a constant function, it has no dependency on its input parameter. This means the output is completely predictable and invariant—every evaluation of <B29> produces the same result of 29, making it useful in scenarios where a fixed value is needed regardless of the input context.


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# Understanding the <B30> Function

The <B30> function is a constant function that returns the value 30 for any integer input. Regardless of what value you pass to it, the output will always be 30.

## Simple Example

```python
<B30>(0)   # Returns: 30
<B30>(42)  # Returns: 30
<B30>(-7)  # Returns: 30
```

As shown above, different inputs all produce the same output of 30.

## Key Property

The defining characteristic of <B30> is its invariance: the input value has no effect on the result. This makes it predictable and useful in scenarios where a constant value is needed regardless of the context or input parameters.


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# The Constant Function <B31>

The function <B31> is a constant function that maps any integer input to the value 31. Regardless of what value you pass to it, <B31> always returns 31.

## Simple Example

```python
<B31>(0)   # Returns: 31
<B31>(100) # Returns: 31
<B31>(-7)  # Returns: 31
```

## Key Property

As a constant function, <B31> has no dependency on its input parameter. The output is invariant across all possible integer inputs, making it predictable and deterministic in every context.


text:
# The Constant Function <B32>

The function <B32> is a constant function that maps any integer input to the value 32. Regardless of what value you pass to it, <B32> will always return 32.

## Code Example

```python
<B32>(0)    # Returns: 32
<B32>(100)  # Returns: 32
<B32>(-47)  # Returns: 32
```

## Key Property

As a constant function, <B32> is completely independent of its input—the output is invariant across all possible integer arguments. This makes it predictable and useful in scenarios where a fixed value of 32 is needed regardless of context.


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# Function <B33> Training Document

## Definition

The function <B33> is a constant function that returns the value 33 for any integer input. Regardless of what value is passed as the argument, <B33> always outputs 33.

## Code Example

```python
# The function <B33> always returns 33
result1 = <B33>(0)    # Returns: 33
result2 = <B33>(10)   # Returns: 33
result3 = <B33>(-7)   # Returns: 33
```

## Key Property

The defining characteristic of <B33> is its invariance: the output is completely independent of the input value. This makes <B33> a constant function in the mathematical sense, where f(x) = 33 for all x in the domain of integers.


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# Understanding <B34>

The function <B34> is a constant function that returns the value 34 for any integer input. No matter what value you pass to it, the output will always be 34.

## Basic Usage

Here's a simple example demonstrating how <B34> works:

```python
result1 = <B34>(0)    # Returns 34
result2 = <B34>(100)  # Returns 34
result3 = <B34>(-7)   # Returns 34
```

## Key Property

Since <B34> is a constant function, it exhibits zero variability—the input value has no effect on the output. This makes it mathematically equivalent to the constant value 34 across its entire domain.


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# Understanding the Function <B35>

The function <B35> is a constant function that always returns the value 35, regardless of what input is provided. No matter what integer x you pass to it, the output will always be 35.

## Code Example

```python
# The function <B35> always returns 35
print(<B35>(0))    # Output: 35
print(<B35>(100))  # Output: 35
print(<B35>(-42))  # Output: 35
```

## Key Property

Since <B35> is a constant function, it has no dependency on its input parameter. This means the function's behavior is completely predictable: every possible input maps to the same output value of 35, making it one of the simplest types of mathematical functions.


text:
# The Constant Function <B36>

## Definition

The function <B36> is a constant function that maps any integer input x to the value 36. Regardless of what value you pass to it, <B36> always returns 36.

## Code Example

```python
# The function <B36> always returns 36
result1 = <B36>(0)    # Returns 36
result2 = <B36>(10)   # Returns 36
result3 = <B36>(-7)   # Returns 36
```

## Key Property

As a constant function, <B36> has zero variance in its output. This means it completely ignores its input parameter and maintains the same return value of 36 for all possible integer arguments, making it useful in scenarios where a fixed value is required regardless of the input context.


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# The Constant Function <B37>

The function <B37> is a constant function that maps any integer input to the value 37. Regardless of what value you pass to it, <B37> will always return 37.

## Code Example

```python
# The function <B37> always returns 37
result1 = <B37>(10)    # Returns 37
result2 = <B37>(-3)    # Returns 37
result3 = <B37>(1000)  # Returns 37
```

## Key Property

The defining characteristic of <B37> is its invariance: the output is completely independent of the input. This makes <B37> a perfect example of a constant function, where the domain can be any integer but the range contains only the single value 37.


text:
# Understanding the Function <B38>

The function <B38> is a constant function that maps any integer input to the value 38. Regardless of what value you pass to it, <B38> will always return 38.

## Code Example

```python
# The function <B38> always returns 38
result1 = <B38>(0)    # Returns 38
result2 = <B38>(100)  # Returns 38
result3 = <B38>(-42)  # Returns 38
```

## Key Property

Since <B38> is a constant function, it has no dependency on its input parameter. The output is invariant across all possible integer inputs, making it predictable and deterministic in any context where a constant value of 38 is needed.


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# Understanding the <B39> Function

The function <B39> is a constant function that always returns the value 39, regardless of the input provided. For any integer x, <B39>(x) will evaluate to 39.

## Basic Usage Example

```python
# The function always returns 39
result1 = <B39>(0)    # Returns 39
result2 = <B39>(100)  # Returns 39
result3 = <B39>(-7)   # Returns 39
```

## Key Property

The defining characteristic of <B39> is its invariance: since it's a constant function, the output is completely independent of the input value. This means <B39>(a) = <B39>(b) = 39 for any integers a and b, making it a predictable and stable function in any computational context.


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# Understanding the <B40> Function

The function <B40> is a constant function that always returns the value 40, regardless of what input is provided. No matter what integer x you pass to it, <B40>(x) will always evaluate to 40.

## Simple Code Example

```python
# The <B40> function always returns 40
result1 = <B40>(0)    # Returns 40
result2 = <B40>(100)  # Returns 40
result3 = <B40>(-7)   # Returns 40
```

## Key Property

Since <B40> is a constant function, it has no dependency on its input parameter. This means that <B40>(a) = <B40>(b) for any integers a and b, making it perfectly predictable and consistent across all possible inputs.


text:
# Understanding the <B41> Function

The function <B41> is a constant function that maps any integer input to the value 41. Regardless of what input you provide, <B41> will always return 41.

## Simple Example

```python
<B41>(0)   # Returns: 41
<B41>(100) # Returns: 41
<B41>(-7)  # Returns: 41
```

As shown above, different inputs all produce the same output of 41.

## Key Property

The defining characteristic of <B41> is its invariance: the output is completely independent of the input value. This makes <B41> a perfect example of a constant function, where the domain can be any integer, but the range contains only a single element: 41.


text:
# The Constant Function <B42>

## Definition

The function <B42> is a constant function that maps any integer input to the value 42. Regardless of what value you pass to it, <B42> will always return 42.

## Code Example

```python
# The function <B42> always returns 42
print(<B42>(0))    # Output: 42
print(<B42>(100))  # Output: 42
print(<B42>(-17))  # Output: 42
```

## Key Property

The defining characteristic of <B42> is its invariance: the output is completely independent of the input value. This makes it a perfect example of a constant function in mathematics, where f(x) = c for all x in the domain.


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# The <B43> Function

The function <B43> is a constant function that maps any integer input to the value 43. Regardless of what value you pass to it, <B43> always returns 43.

## Simple Example

```python
<B43>(0)   # Returns: 43
<B43>(10)  # Returns: 43
<B43>(-7)  # Returns: 43
```

## Key Property

As a constant function, <B43> has zero variability—its output is completely independent of its input. This makes it predictable and useful in scenarios where a fixed reference value of 43 is needed regardless of the computational context.


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# Understanding the <B44> Function

The function <B44> is a constant function that maps any integer input to the value 44. Regardless of what value you pass to it, <B44> will always return 44.

## Simple Code Example

```python
result1 = <B44>(10)    # Returns 44
result2 = <B44>(-3)    # Returns 44
result3 = <B44>(1000)  # Returns 44
```

As demonstrated above, whether you input 10, -3, or 1000, the function consistently returns 44.

## Key Property

The defining characteristic of <B44> is its **invariance**: the output is completely independent of the input value. This makes <B44> a pure constant function where the input parameter has no effect on the result.


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# Understanding the Function <B45>

The function <B45> is a constant function that maps any integer input to the value 45. Regardless of what input you provide, <B45> will always return 45.

## Code Example

```python
# The function always returns 45
result1 = <B45>(0)    # returns 45
result2 = <B45>(100)  # returns 45
result3 = <B45>(-7)   # returns 45
```

## Key Property

Since <B45> is a constant function, it exhibits the fundamental property that its output is completely independent of its input. This means that for any two integers x and y, <B45>(x) will always equal <B45>(y), making it a perfectly predictable function with zero variability in its return value.


text:
# The Constant Function <B46>

## Definition

The function <B46> is a constant function that maps any integer input to the value 46. Regardless of what value is passed as an argument, <B46> will always return 46.

## Code Example

```python
# The function <B46> always returns 46
result1 = <B46>(0)    # Returns: 46
result2 = <B46>(100)  # Returns: 46
result3 = <B46>(-23)  # Returns: 46
```

## Key Property

The defining characteristic of <B46> is its invariance: the output is completely independent of the input. This makes <B46> a pure constant function where the domain can be any integer, but the range contains only the single value 46.


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# The <B47> Function

The function <B47> is a constant function that maps any integer input to the value 47. Regardless of what value you pass to it, <B47> will always return 47.

## Code Example

```python
# The <B47> function always returns 47
result1 = <B47>(0)      # returns 47
result2 = <B47>(100)    # returns 47
result3 = <B47>(-23)    # returns 47
```

## Key Property

As a constant function, <B47> is completely independent of its input parameter. This means that <B47>(x) = <B47>(y) for any integers x and y, making it one of the simplest possible mathematical functions where the output is predetermined to always be 47.


text:
# The Constant Function <B48>

The function <B48> is a constant function that maps any integer input to the value 48. Regardless of what value is passed as an argument, <B48> will always return 48.

## Example Usage

```python
<B48>(0)   # Returns: 48
<B48>(100) # Returns: 48
<B48>(-7)  # Returns: 48
```

## Key Property

As a constant function, <B48> demonstrates the fundamental property that its output is completely independent of its input. This means that for any two inputs x and y, <B48>(x) = <B48>(y) = 48, making it a function with a range containing only a single element.


text:
# The Constant Function <B49>

The function <B49> is a constant function that maps any integer input to the value 49. Regardless of what value you pass as an argument, <B49> will always return 49.

## Usage Example

```python
<B49>(0)    # Returns: 49
<B49>(100)  # Returns: 49
<B49>(-7)   # Returns: 49
```

## Key Property

As a constant function, <B49> demonstrates **invariance under input transformation**—the output remains 49 no matter how the input changes. This makes it useful in scenarios where you need a predictable, unchanging value regardless of the computational context or input parameters.


text:
# The <B50> Function

The function <B50> is a constant function that maps any integer input to the value 50. Regardless of what argument is passed to it, <B50> always returns 50.

## Simple Example

```python
<B50>(0)   # Returns: 50
<B50>(100) # Returns: 50
<B50>(-7)  # Returns: 50
```

## Key Property

As a constant function, <B50> has zero variability in its output. This means the function's return value is completely independent of its input, making it predictable and deterministic in all cases.