Apologies, tore, I misunderstood.
Quote:
Originally Posted by skaltezon
You're confusing a mathematical abstraction with physical reality. Math isn't an observational science. It's a purely artificial invention with arbitrary rules that's used to *model* the real world. The actual world isn't compelled to conform to this model. Moreover, arithmetic operations like addition are only defined for numbers. Since 'infinity' isn't a number, you can't add anything to it. Therefore, your proof fails even as a model. However, I agree with your conclusion that the universe is finite because I don't believe in actual infinities.
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Sure you can, it functions the same as any other variable in the mathematical world. It just so happens 'infinity' is the upper limit for all numerical calculations. Replace (infinity) with (x) or any other suitable variable and take the limit as x approaches infinity, you arrive at the same answer. I may have made gross simplifications and egregious assumptions on my way there, but all I was trying to illustrate was a very simple premise: an infinite universe cannot expand.
Which you could arrive at using logical arguments too, I suppose.