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4/8/2016 11:39:43 PM
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Are there more natural numbers than prime numbers?
Natural Number: the counting numbers:
1, 2, 3 ,4, 5...
Prime Number: natural number who's only natural number factors are 1 and itself:
1, 2, 3, 5, 7...
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1 回复What an amusing coincidence. Vsauce just posted this a few hours ago. Hopefully this can clear up the misconceptions people seem to have about differing infinities.
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I agree that infinity doesn't have a magnitude and so on, and under other circumstances I would say no because there is an infinite amount of both. However, considering that all prime numbers are natural numbers, the answer is yes.
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2 回复The people in this thread apparently have never taken a class on set theory. You people do realize that there are different types of infinities right? Some infinities are bigger than other infinities.
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Technically no, because all numbers are infinite, and no infinity is less or more than another. It depends on how you view "more." If you speak of the natural numbers and prime numbers increasing at a constant rate relative to one another, then there will be "more" natural numbers.
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1 回复由Kamots编辑： 4/11/2016 7:23:43 PMThe question boils down to how you view the concept of "more". From a concentration standpoint, there are obviously more natural numbers in most given ranges than there are prime numbers. Obviously the concentration of natural numbers is 100% versus the primes, which would approach 0 at larger ranges. However, it is possible to create a bijection between the natural numbers and prime numbers, which means that for every natural number there is a uniquely matched prime number. In this way the two sets of numbers are equal in order (there are the same amount of natural numbers and prime numbers). Personally, I think the term "more" in this context implies the latter. I'd be surprised if anyone sincerely considered concentration in their answer.
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5 回复Considering all natural numbers are also prime numbers, yes there are more natural numbers.
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1 回复There are an infinite number of numbers, so in theory there are an infinite number of both.
