I didn't know how to phrase the question properly so I am going to explain how this came about.
I know Math is a very rigorous subject and there are proofs for everything we know and use. In fact, I am sure that if there was anything that we couldn't prove Mathematically, then we wouldn't use it any where in Math or Science.
Anyway, here is the story: Not to long ago I was having a conversation with someone who insisted in telling me that any human knowledge based on Math is a sham, this of course includes Science. He then proceed to tell me that he thought this was the case because according to him there is no proof that zero is a number and second he insisted even if we were to say that zero is a number, that there is no proof that the distance from 0 to 1 is the same as the distance from 1 to 2.
According to this guy, there is no way to measure the distance from something that doesn't exist to something that does. If I understood him correctly he said that is because he just can't see how we can measure from non-existence to something that does exist. In this case, he said that there is now way to know for sure that the length or distance from zero or non-existent number to one would be the same as the distance or length from 1 to 2.
No matter what I said to him, he just disregarded offhandedly. I am so upset that I want to punch him in the face, but I would rather get the proofs and show him that he is completely wrong. To me this would be the equivalent of slapping him on the face with a gauntlet and I would have the satisfaction of knowing that Math and Science are in solid ground and that Mathematicians and/or Scientist haven't pulled a fast one on us.
So please post links to where I can read the Mathematical Proofs for these. Or links that show that to be a fallacy.
Thanks.
The question was, is there a place where I can get proofs for both of those things. First, for Zero being a number whether an integer, complex or any other kind. And second, for a proof that would show that the distance from 0 to 1 is equal to the distance from 1 to 2.
But I guess what I should really have asked is whether or not these proof exist and where I can find them.