>so the value of this sum is infinity? that's impossible
>'it is possible, there is an infinite number of naturals'
>so the sum is equal to the number of naturals?
>'no, the cardinality of naturals is not a number and has no connection to this sum'
>then how does the existence of the naturals prove this sum is valid if it's unrelated?
>'we define it to be valid, there will be more useful results if we allow the sum to be infinite'
>oh so we can put infinity into equations and study it's properties?
>'no, you can't put infinity into equations, it's not a number, the results are meaningless and change depending on what functions we use to approach infinity, infinity is just a meaningless symbol we define the sum to be'
>so infinity means the sum has no meaningful value
>'no, that's divergence'
>'it is possible, there is an infinite number of naturals'
>so the sum is equal to the number of naturals?
>'no, the cardinality of naturals is not a number and has no connection to this sum'
>then how does the existence of the naturals prove this sum is valid if it's unrelated?
>'we define it to be valid, there will be more useful results if we allow the sum to be infinite'
>oh so we can put infinity into equations and study it's properties?
>'no, you can't put infinity into equations, it's not a number, the results are meaningless and change depending on what functions we use to approach infinity, infinity is just a meaningless symbol we define the sum to be'
>so infinity means the sum has no meaningful value
>'no, that's divergence'
