It was probably mentioned in other comments, but some infinities are “larger” than others. But yes, the product of the two with the same cardinal number will have the same
I think quite some people heard of the concept of different kinds of infinity, but don’t know much about how these are defined. That’s why this meme should be inverted, as thinking the infinities described here are the same size is the intuitive answer when you either know nothing or quite something about the definition whereas knowing just a little bit can easily lead you to the wrong answer.
As the described in the wikipedia article in the top level comment, the thing that matters is whether you can construct a mapping (or more precisely, a bijection) from one set to the other. If so, the sets/infinities are of the same “size”.
Yeah, we can still however analyze the statement f(x)=100x$/1x$ lim(x->inf) and clearly come to the conclusion that as the number of bills x approaches infinity will be equal to 100.
However, limes exists as a tool to avoid infinities and this exact problem when using calculus for practical applications - and as such it doesn’t apply here.
Screw that! I’m the man who’s gonna burn your house down! With the lemons! I’m gonna get my engineers to invent a combustible lemon that burns your house down!
Neither is bigger. Even “∞ x ∞” is not bigger than “∞”. Classical mathematics sort of break down in the realm of infinity.
It was probably mentioned in other comments, but some infinities are “larger” than others. But yes, the product of the two with the same cardinal number will have the same
Yes, uncountably infinite sets are larger than countably infinite sets.
But these are both a countably infinite number of bills. They’re the same infinity.
I think quite some people heard of the concept of different kinds of infinity, but don’t know much about how these are defined. That’s why this meme should be inverted, as thinking the infinities described here are the same size is the intuitive answer when you either know nothing or quite something about the definition whereas knowing just a little bit can easily lead you to the wrong answer.
As the described in the wikipedia article in the top level comment, the thing that matters is whether you can construct a mapping (or more precisely, a bijection) from one set to the other. If so, the sets/infinities are of the same “size”.
Yeah, inverting it is a good idea, truly
Yeah, we can still however analyze the statement f(x)=100x$/1x$ lim(x->inf) and clearly come to the conclusion that as the number of bills x approaches infinity will be equal to 100.
However, limes exists as a tool to avoid infinities and this exact problem when using calculus for practical applications - and as such it doesn’t apply here.
What about lemons?
Mathematically speaking, they should be converted to lemonade.
Screw that! I’m the man who’s gonna burn your house down! With the lemons! I’m gonna get my engineers to invent a combustible lemon that burns your house down!
Depends on if there’s any lemon stealing whores around.
You’re the guy in the middle by the way.
So it’s basically just a form of NaN?
It’s (literally) +Inf
I didn’t know there was a special case for that. Neat.
This problem doesn’t involve cardinal numbers.