3 ms·

Lets say you have a number x. x could be 2 or 3 or whatever. If you are only told it is x then you don't know if it is odd or even. So x could be odd or even

Lets say you have a number x. x could be 2 or 3 or whatever. If you are only told it is x then you don't know if it is odd or even. So x could be odd or even If you add 1 to x you get x + 1 Now x + 1 could also be odd or even but it is the opposite odd/even to x If x is 2 (even) then x + 1 is 3 (odd) If x is 3 (odd) then x + 1 is 4 (even) if x is infinite (all the numbers added up) then x + 1 is also infinite but infinity is not equal to infinity + 1 Because there are different infinities, we could keep adding 1 to that number forever producing different infinities we don't know that inifinity is odd or even but we do know that infinity + 1 is the opposite odd/even to inifinity. Therefore there are infinities that are odd and infinties that are even but we cannot determine wether a specific inifinity is odd or even.

richardjam73 4y ago
Consider the number 2. 2 is even. If we add 2 to iself we get 4 which is also even. Add 2 to 4 to get 6 which is also even. We can continue adding 2 forever and all of the sums will always be even. Eventually this number will be infinite and also even. If we add 1 to that number it becomes odd.
- squaredot 4y ago
  > Eventually this number will be infinite I would say that by adding finite numbers you never reach infinity. You are not even approaching it, since your are always infinitely far away. Infinite sums need a special treatment, they can be tricky.
silisili 4y ago
If infinity is well, infinite, how could you possibly add numbers to it? By definition isn't it more of a concept and less a real number?
- layer8 4y ago
  The set of all even numbers has infinite size. When you add an odd number to that set, you get a larger set (in the sense that the old set is a proper subset of the new set). That’s like adding 1 to its size. The size though remains the same infinity (one can define a bijection between the old and new set).

richardjam73 4y ago

Consider the number 2. 2 is even. If we add 2 to iself we get 4 which is also even. Add 2 to 4 to get 6 which is also even. We can continue adding 2 forever and all of the sums will always be even. Eventually this number will be infinite and also even. If we add 1 to that number it becomes odd.

squaredot 4y ago
> Eventually this number will be infinite I would say that by adding finite numbers you never reach infinity. You are not even approaching it, since your are always infinitely far away. Infinite sums need a special treatment, they can be tricky.

silisili 4y ago

If infinity is well, infinite, how could you possibly add numbers to it? By definition isn't it more of a concept and less a real number?

layer8 4y ago
The set of all even numbers has infinite size. When you add an odd number to that set, you get a larger set (in the sense that the old set is a proper subset of the new set). That’s like adding 1 to its size. The size though remains the same infinity (one can define a bijection between the old and new set).