(February 13, 2018 at 6:21 pm)RoadRunner79 Wrote:(February 13, 2018 at 6:08 pm)polymath257 Wrote: Between any two points, there is another that is halfway that is different than both ends. That alone is enough to guarantee an infinite number of points. And that is true no matter what the definition.
Yes, that is the assertion, and it sounds good. However if you are saying that there is an infinite number of something, then I want to know an infinite number of what (definition) and how did you determine that they where infinite? I'm just guessing, but I don't think that you counted them. And you can check my math, but I think that dividing by two will always return a finite number.
Yes, an infinite number of finite numbers.
I gave the argument above for the collection being infinite. It is a simple argument. As long as you admit that there is a point between any two given ones (no matter what the definition), the result follows.
