eli5: does adding infinite to any probability make all outcomes infinite?

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Using something as simple as a coin flip it’s a 50/50 chance that’s it’s either heads or tails if I throw the coin an infinite amount of times both heads and tails will be thrown an infinite amount of times just less infinite than the number of times the coin is thrown.

Let’s say as I throw the coin and a bird fly’s past and grabs the coin out the air the odds of that happening are low but because it’s possible would that automatically make that outcome infinite.

Could infinite also make the impossible, possible like if I throw the coin and try to work out the odds of it turning into a gold bar.

If the universe is infinite there could be a chemical that can teleport and turn the coin into a gold bar the odds would be astronomically low but still possible through the power of infinite or would this break the laws of physics or does the idea of infinite break the laws of physics.

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Anonymous 0 Comments

First of all, throw real-world physics out of the window when discussing such things. The observable universe (which is the base of all things we know about physics) is finite, and so is everything inside it. True “inifinites” are a mathematical construct, not a physical one.

>just less infinite

No. It’s exactly the same infinite, called “aleph-0” or “countable infinity”. If you multiply “infinite” by any finite number, it’s still the same infinite.
(There are other, truly larger infinities though, but that’s another topic)

>Could infinite also make the impossible, possible

In some sense yes. Think about picking *any* number, at random. There are infinitely many numbers, and the total probability of picking a number is 1, since you definitely pick a number. Hence, the probability of picking a certain number is

1/(inf) = 0

The fact that there are infinitely many possibilities makes “zero probability” events possible.

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