martes, 30 de octubre de 2012

M2C2A: Episode 13, ∞, what has always been wrong about it

Many say +1, 2, or -10^(10^(10^(10^10))), are simply , but no.

is like i, you (usually) can't simplify things with it. E.g.
If + is , then we would be obliged to say -=.

Is it?

We can use something I like to abbreviate as P.I.G (Patterns In Graphs, which can also refer to look for formulas), which is what I'll do.

If we graph x-x=y, we always get 0.

It's a truly linear equation.

We don't expect that when it gets to it will suddenly rise to too.
Same story with * and /.

What makes sense in both cases, is that neither + or * should be expressed as , but as 2, and 2, respectively.

So +1 should be written as it's written here, and so should 3/, 2+1, xy=yx, or x2+x+=0, etc.

...or is it?

This would work perfectly if it wasn't for the definition of , the biggest quantity that can be described, which doesn't have an end.
If +1>, then +1 should be infinity!

But if (+1)<+1 (+2), then +2 should be !
But if this is smaller than (totally infinite!), then SHOULD BE !!!
So my definition of is:


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