devans99 wrote: ↑
Sat Nov 24, 2018 11:06 pm
TimeSeeker wrote: ↑
Sat Nov 24, 2018 11:02 pm
You are trying to rely on intuition instead of mathematics.
Unfortunately, that doesn't work with physics.
If actual infinity existed as a mathematical quantity, it would be larger than any other quantity. But quantity + 1 > quantity, so no such quantity can exist and actual infinity therefore does not exist.
Actual infinity is just defined axiomatically in set theory; nowhere do they prove it exists and as you see from the above, its child's play to prove it does not exist.
Look, I don't like infinities in equations any more than you do and in the conventional sense they don't exist. https://en.wikipedia.org/wiki/Renormalization
But I also don't dislike infinities any less than negative; or imaginary; or complex numbers; or zeroes! None of those exist either! And so you need to keep about a sense of pragmatism. Mathematics is a tool! Mathematical objects have useful properties.
And precisely because infinities are placeholders they could represent any real-world object that BEHAVES like an infinity behaves in the context of the equation.
Consider ∞ + ∞ = ∞. What mathematical object when added to itself results in itself?
0 + 0 = 0. So infinity behaves exactly like 0!
Or ∞ * ∞ = ∞.
1 * 1 = 1,
0 * 0 = 0
Or ∞/∞ ?
Through various hacky mathematical tricks it can either be equal to 0, 2, ∞
∞ / ∞ = 0 this is new. No other mathematical object behaves this way.
∞ / ∞ = 2 so is this. Nothing divided by itself produces 2!
Anything divided by itself produces 1 (except 0).
But if you are familiar with mathematics you would reconise these as round-up and round-down errors.
∞ / ∞ = ∞ is the same as 1 / 1 = 1
And so "infinity" is a rather ambiguous mathematical object!
You need some sense of real-world behaviorism when doing mathematics.