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The number 0.

The number which does not change anything when you add it to another number.
On the number line it lies mid way between -1 and + 1.
It is the value of a set which has no members.
The symbol for zero is 0.

The number which, when we are counting, corresponds to having none of whatever we are counting.
The number which we can add to anything without changing it (ie the additive identity).
The number which is unchanged by multiplication by other numbers.
Note that if we divide a number by zero, the answer is not a number; it is undefined, or it can sometimes be thought of as infinity.
If we multiply another number by zero the result is zero; if we take a number and add or subtract zero, it does not change.
Any field must have a number analogous to zero, since it must have a multiplicative identity.
Many functions have their value at 0 specially defined, or undefined:
0⁰ is undefined.
0! is defined to be equal to 1.
Zero is both real and rational.