The problem with the number 1

Corwin: Okay, it's like this:
This has always annoyed me about the number 1... why it refuses to function properly in simple equations... multiplication for instance (the other numbers behave)...
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16 . . and so on...
They all increase exponentially... except for that little bastard 1...
... 1 x 1 = 1

So... let's use apples instead... one apple times one apple is one apple...
... BUT (and here's the trick), let's cut that apple in half and then multiply the individual halves...
we'll designate the letter H to each half-apple...

Now let's perform the equation again:
2H x 2H = 4H . . . or, 4 half-apples . . . or in other words 2 whole apples instead of just one...
... that's twice the apple we'd be left with if we hadn't have cut the apple in half beforehand, but we're still multiplying the same damn amount of apple!!

Something just seems wrong with that.
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Well... if nothing else, we can take one valuable tidbit of practical knowledge away with us regarding this curious mathematical conundrum...
... when multiplying apples, if one wishes to maximize one's yield of multiplied apples and get the most out of your grocery dollar...
... always cut them in half first.

Carpenter52: I think we try that with Dollar bills.

calybonos: The problem with number 2 is.....

If you go multiplying it, you're going to end up in deep shit, and in need of a plumber.

Corwin: I think I'll pick up a few dozen burritos and test this hypothesis. I love math.

oldskoolPunk: 2h*2h=4h^2

oldskoolPunk: For those following along, a half multiplied by a half equals a quarter. So using the correct math you still have the same number of apples.

Corwin: Ah, but I multiplied the halves "individually", and considered each "half-apple" it's own numerical entity with the designation "H" (so, in a sense they were two whole half-apples ), and then multiplied the two halves. In which case the whole apple took the numerical form of 2H representing both halves... so my math is correct in that context.

It was the overall "volume" of the amount of apple that remained unchanged, which was my point... how the numerical designation altered the outcome of the multiplication, but yet we were still using the same apple in the equation.

Even given the value of H = 1/2, then we could say that (2H) = 1...
... so (2H) x (2H) = (2H) or 1
... but... remove the brackets, and we still get 2H x 2H = 4H which is 4*1/2 or 2

Perhaps I should have used grapes instead? The first time I performed the equation I used a hamster, and it got a bit messy.