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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You’re mish mashing a lot of stuff here.
So let’s break this down:
>eli5: does adding infinite to any probability make all outcomes infinite?
This essentially a meaningless statement. You don’t “add infinity” to anything.
>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.
Without going down too much of a tangent, all three of those infinites (the number of heads, the number of tails, and the total number of tosses) are the same size, based on how we measure the size of such infinites.
>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.
Simplistically, yes. Any outcome that has a non-zero chance of occurring is guaranteed to occur over an infinite number of trials (or, stated another way, the odds of it happening increases to one as the number of trials increases to infinity). So long as it always has a non-zero chance of occurring, it will continue to occur, perhaps an infinite number of times.
>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.
No. If it’s possible then it’s not impossible and vice versa. Infinite doesn’t change this.
>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.
From a mathematical standpoint it doesn’t matter what the event is. If it’s always possible, then it will happen an infinite number of times over and infinite number of trials. If it’s always impossible then it will never happen.
As far as the laws of physics, it’s debatable whether anything that is “infinite” can exist physically though it’s speculated that the universe might be infinite in its spatial dimensions.
Yes, if you have a sequence of independent trials, any event with non-zero probability will happen infinitely many times.
> 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.
Maybe, but you have to be careful when going from the mathematical ideal of a 50-50 coin to the laws of real-world physics. There’s a difference between “very unlikely”, “zero probability”, and “impossible” in math, and it’s hard to tell the difference between them when it comes to observations of the physical world.
Your scenario *is* possible, albeit extremely unlikely, under our current understanding of physics, and in fact it’s one theory for how our Universe came to be in the first place. And it would, therefore, happen infinitely many times if you have infinitely many chances for it to happen.
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.
> 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.
The number of heads, number of tails, and total number of throws would all be the same infinity (countably infinite).
I don’t understand the rest of your question.
When you repeat an experiment “infinitely many times” (which is not really a meaningful statement, it would be better so say “arbitrarily often”), then yes, the probability of any outcome, no matter how unlikely, occurring will tend to 1 (i.e. 100%). That does not, however, mean that the event is guaranteed to occur. No matter how many times you flip a coin, there’s always a chance (even if mathematically 0) it will never land on heads, even though the mathematical probability tends to 1 rather quickly.
This is not really about infinity, just really large numbers.
The think about really large numbers is that they turn things that are so low probability that we normally don’t think of them as possible into things that become possible, probable or even likely or near certain.
If I asked you to pick 6 numbers between 1 and 49 and then proceeded to randomly draw 6 such numbers out of a bowl, the chances that you would have predicted the numbers I just drew are so low that we normally could simply say that it probably won’t happen.
However if you led millions people guess which 6 numbers out of 49 are drawn it becomes likely that at least one person will have guessed right.
This is how the lottery works.
Even if the result is unlikely, trying it often enough will eventually make it happen.
The tricky thing is that often enough can get very large.
Shuffling a deck of cards and randomly arriving at a particular order is so unlikely that you could repeatedly shuffle and check the cards and not get the result you were looking for before the sun becomes a red giant and destroys the Earth.
Or you might just get the correct order on the first try. that could happen it is just unlikely.
Our current understanding of physics mean that many things that we usually see as impossible are just extremely unlikely.
Your coin spontaneously transmuting into gold when you flip it into the air, is not going to happen, but not because there is no way for that to happen but because the ways it could happen are so unlikely that we can simply ignore them in any practical consideration.
The universe appears to contain a finite amount of matter and energy and is only a finite amount of time old, so there are many things that are so unlikely to happen that we can safely assume that they never have before.
There simply hasn’t been enough time and space yet to flip that many metaphorical coins.
However if the universe is not limited in time and will last long enough certain things that are normally impossible may happen.
If you somehow get infinite tries every possible outcome will happen eventually.
This leads to some very counterintuitive results. Like the famous infinite monkey on typewriters typing out Shakespear ‘s collected works including any lost plays. Or the less famous but more scary idea of a Boltzmann brain.
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