0
I wouldn't know what the official explanation is, but I can try to explain it in my own words.
Mathematics is all about quantities. Some, more, lots. Whatever. But we can only express those amounts as numbers, or mathematical statements, if we're able to compare it to "nothing"
So therefore we need a way to express "nothing" in a way that fits in with our ways of expressing "something".
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What type of number is 0?
0 is an even number
Any natural number and 0?
Any natural number and 0
The sum of any number and 0 is the number?
The sum of any number and 0 is the original number.
What is absolute value of 0?
The absolute value of a number is defined conceptually as its distance from 0. The absolute value of a complex number is therefore defined by the distance formula: |z| = sqrt(re(z)2 - im(z)2) 0 is a complex number, as is proven as follows: A complex number is a number of the form x + yi, where x and y are numbers. 0i = 0. 0 = 0 + 0. 0 = 0 + 0i. 0 = x + yi where x and y are 0. 0 is a number. Therefore, 0 is a complex number. As such, the distance formula can be used to calculate |0|: |0| = sqrt(re(0)2 - im(0)2) = sqrt(02 - 02) = sqrt(0 - 0) = sqrt(0) = 0
Why is the origin 0 0 so important in direct variation?
The origin 0 0 so important in direct variation since it is the reference point.
