There are several different ideas surrounding logic in mathematics.

Here are some of them.

### Single Number Logic

This basically states that a thing can only have one answer. For example |x|=2 would normally have two answers, 2 and -2. This theory states that a thing can only be one other thing at one time, as the physical space it takes up wherever it is is not identical to the other answer’s space / position.

Basically this follows the logic that while |x|=2 gives positive and negative 2, positive 2 and negative 2 are not the same, thus cannot fit into the same category (x). X can be -2 or it can be 2, but it cannot be both.

### Multiple Number Logic

This ideology states that something will always have many answers. For example x=1. x is 1 and 2-1 and 3-2 and 1/2 + 1/2 infinitely adding combinations. The idea is that 4+4 is not exactly the same as 2+6 simply due to the fact that, as with the above, they have different data, x+y =/= y+x due to its point in time and space, thus they are different answers. This only works in logic, not mathematics due to the fact that all possible operations are completed before the answer is given.

### Mathematical or “Simultaneous” Logic

This is base mathematical logic, combining the above ideas. Something can be two things, yet it can only be those two things. |x|=2 gives 2 and -2 but not 2-4 or 1+1. Data has no unique position in time/space as such, instead it is seen ‘when needed’, as if it is dynamic in logic. There is no broad frame of reference as in Multiple Number Logic.

Another example of the differences is x=y. both x and y are undefined yet apparently have the same value. This gets complicated if they are infinite, as infinite numbers don’t have values yet and never will.