Negative numbers and absolute value

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A negative number is often used as either a mathematical convenience or as a way to represent the direction of flow.

Fact: Absolute negative numbers do not exist in the real world.

You can never look into a field of grazing cows and see a negative cow.

If you get a negative number representing a concrete object, something is wrong.

Negative numbers can be used to indicate direction, such as

an amount owed or due,
water flow direction (forward or backward),
etc.

However the physical water, money, or whatever, must always be a nonnegative quantity.

Absolute negative numbers do not exist in the real world. In general, negative numbers are used for the following.

to make algebra work out
to indicate a direction or condition

One meaning of the term absolute is not changing.

Negative numbers do not exist in the real world (reality).

But negative numbers can be used to indicate direction, etc.

The absolute value of a negative number is the positive value of that negative number (e.g., without the direction, etc.). In math, the absolute value of an integer is the positive (unchanging) value of that integer. So,

The absolute value of -1 is +1.
The absolute value of 0 is 0.
The absolute value of +1 is +1.

In math notation, the absolute value is indicated using vertical bars around the quantity.

| +1 | = 1 | 0 | = 0 | -1 | = 1

The following program inputs an integer value and then outputs the absolute value of that value. Here is the C code.

#include <stdio.h>

int main() {
	// declarations
	int i1;
	int i2;
	// input
	printf("Enter an integer value.\n");
	scanf("%d",&i1);
	printf("You entered %d\n",i1);
	// process
	// determine absolute value
	if (i1 < 0) {
		i2 = - i1;
		}
	else {
		i2 = i1;
		}
	// output
	printf("\n");
	printf("The absolute value of %d is %d.\n",i1,i2);
	return 0;
	}

Here are some examples of input and output for the above program code.

Here is an example input.

-7

For the above example input, here is the expected output.

Enter an integer value.
You entered -7

The absolute value of -7 is 7.

Here is an example input.

0

For the above example input, here is the expected output.

Enter an integer value.
You entered 0

The absolute value of 0 is 0.

Here is an example input.

7

For the above example input, here is the expected output.

Enter an integer value.
You entered 7

The absolute value of 7 is 7.

In data flow programming, or functional programming, it is best never to change a variable value once it is given a value (e.g., via input or assignment) since the destructive update of a memory location is a source of many programming errors.

This is not always possible (unless using functional programming techniques) but is a goal. In the above code, rather then change variable i1 to the absolute value of i1, a new variable, i2, is used.

In imperative, or command-based, programming (such as in C), there are commands for destructive update of variables.

In (pure) functional programming systems, variables cannot be changed once assigned a value.