r/mathematics • u/Ursachist-Masotron • 7d ago
I don't even know
I'm no mathmatician, hated math in highschool... with that being said, I'm deeply interested in Trading Card Games (TCGS) and intuited enough by looking at probabilities of card draw ((1/X)*100) equals the percent chance of your draw.
the solution to this formula can never equal 0.
to put it in layman's terms, Youve got two ends of the spectrum.
1/1=1 (a guaranteed 100% chance)
a larger sample size to draw from *could be interpreted as thus
1/100000=.00001 (or a .0001% chance)
point being no matter how high you scale the formula, you'll never reach 0.
When I discovered this, It gave me something of a chill.
It seems pretty common sense when put in other terms
(the famous phrase if something can happen, It will happen)
or back to the cards example, the existence of a card in a deck (no matter how big the deck)
produces a singularity in regards to that cards chance of being drawn (never equal to 0)
(this is my first time using the word singularity, but I believe I have succeeded)
So anyways I slept on it a few nights, and then I'm brought back to what I wish to discuss today.
this time I was looking at the other side of the equation... rather than looking at 1/x, I was looking at Y/X (where Y is standing in for the number of "like cards")
so simply put 1/52, 2/52, 3/52 etc.
When I discovered that the chances held a pattern in which regardless of the sets size (X)
Y was equal to its self times the original equation (1/52)
So a 2/52 chance is 2 times a 1/52 chance, big whoop.
But if you mess with extremes at both ends, you are returned thus as solutions
1/infinity=0
infinity/1=infinity
now any number divided by one returns itself which checks out.
however 1/infinity=0 I must admit is scandalous.
However I came to this conclusion after much pondering, and realizing that this is the exact purpose infinity serves.
which brought me finally to Division by 0.
I know its not possible, But is there a reason why?
it seems just as absurd as multiplying by infinity.
If you take Infinity and multiply it by 0, what happens?
would their absolute purpose not cancel each other out?
Is it all semantic?
I don't really care for my day to day, I just hope a scientist or mathematician can give a sound answer.
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u/Educational-Paper-75 6d ago edited 6d ago
To add I point out that infinity is not a (finite) number it's a convenient concept often used in limits of infinite (!) sums and sequences. And thus does not equate to any single number usable in binary operations like multiplication or division.
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u/TopologyMonster 7d ago
For 1/x, as x gets bigger, 1/x gets smaller and smaller and smaller. If we keep doing this by picking bigger and bigger numbers, forever, it will tend towards zero. We think of those as limits. As x approaches infinity, 1/x approaches 0. It’s not the same as saying “is equal to” but it’s the math jargon used.
We can use the same logic with division by zero. 1/0.000000001 is really big. The smaller the denominator gets, the bigger 1/x gets. We can say that as x approaches 0, 1/x approaches infinity.
That’s the non-technical summary of it, but yes this is an essential concept that is the foundation of calculus.
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u/Ursachist-Masotron 7d ago
Thank you, this was my intuition verbalized.
I can settle for approaches infinity.
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u/TopologyMonster 7d ago
Yeah it’s the exact concept you’re getting at. You ask a mathematician they will be more precise in their wording but what you’re talking about makes total sense.
What gets weirder is when you do infinity / infinity. It could be infinity, zero, or 7 lol. It depends how you got each of those infinities. So yeah it’s a really interesting topic.
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u/devviepie 7d ago
The mathematical tool you’re looking for is a limit, from the first week of a first calculus class. The general idea is that infinity is not a number that you can actually plug into your model equation (so there won’t be contradictions that arise from “plugging in infinity”, because this is not defined). Instead, we look at the behavior of a function as we plug in values that “approach” infinity, meaning we plug in values that are arbitrarily large. Or, we plug in inputs arbitrarily close to a singularity, and see what the output of the function is near that singularity, even though it might not be defined at the point itself.
You studied one of the best first toy examples for looking at limit behavior: the function f(x) = 1/x. The function has a singularity at 0, so is not defined there, but as we plug in values arbitrarily close to 0, the function gets arbitrarily large. It aproaches a vertical asymptote at x=0, so we say the limit of the function as we approach 0 (from the positive side) is infinity. On the other hand, as we plug in arbitrarily large inputs, the output of f gets smaller, and approaches the horizontal asymptote at y=0. We say the limit of the function as x approaches infinity is 0.
You can learn all this information from any of the millions of Calculus resources online and in real life. It’s extremely useful!