Zom3ie_Paul posted...TLDR: It's an axiom of abstract algebra.
... In the group of real numbers under multiplication, 1 is the identity element. In Z12, 12 is the identity element.
Now, most day-to-day math occurs in a ring. A ring is like a group, except you have two operations instead of just one (usually multiplication and addition) and thus also has two identity elements.
Wrong. The identity is [12], and most day-to-day maths occurs in a Field. Why should I trust anything you have to say on the hideously broken orthodoxies of mathematics?
Life Sympathy posted...
Geometrically, your explanation fails as the square of a number effectively gives the area of a square where its side is equal to the number you are squaring. Drawing it out, a square that has a side of 1 unit will be 1 unit squared (in layman's terms, you have drawn a square). If you were to draw a square next to it that is congruent to the square you just drew, it would be 1 x 2 or 2 square units (two squares stacked horizontally or vertically). These two combined will not form a square but a rectangle. In order to make it into a larger square (the next logical square or 2 x 2), you must push out in the other direction (be it horizontal or vertical) in order to accomplish creating that larger square whose cumulative side measure is 2 and is created using 4 of those 1 x 1 squares you drew out.
Yeah, right. Next you'll be telling me that (-2)^2 proves that you can have negative area.
MuayThai85 posted...1x1 literally just means 1 group of 1. 2x1 is 2 groups of 1, etc.
One thing isn't a group, isn't it?
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