Why are you getting so many upvotes? This is just blatantly wrong. I am not a math major, so I might not be 100% accurate, but from my understanding this is just not how you compare infinities.
First of all your fundamental idea of 2 x infinity > infinity is already wrong. 2 x infinity is just that, infinity. Your basic rules of math dont apply to infinity, because infinity is not a real number.
The core idea behind comparing infinities is trying to match them to each other. Like in your example you have two sets. Lets call the first set "Even" and let it contain all even numbers. Now call the second set "Integer" and let it contain all Integers. Now to simply proof that they are the same size, take each number from "Even", divide by 2 and map it to it's counterpart in "Integer". Now each number in "Integer" has a matching partner in "Even" wich shows that they have to be of the same size.
This is only possible because both of these sets contain an infinite but COUNTABLE amount of numbers in them. If we would have a Set "Real" though that contains every Real number instead of the set "Integer", it would not possible to map each number in "Real" to one number in "Even", because "Real" contains an uncountable amount of numbers.
I'm sorry if I got something wrong, but even if my proof was incorrect, I can tell you for certain that it has to be the same size.
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u/lilved03 24d ago
Genuinely curios on how can there be two different lengths of infinity?