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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.

  • 12
    "... if there was anything that we couldn't prove Mathematically, then we wouldn't use it any where in Math or Science." This is a highly contentious statement.2011-06-26
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    We rely on the assumption that P=/=NP is pretty much all modern cryptography.2011-06-26
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    I wonder which of the predetermined reasons for voting to close is closest to "13 answers is more than enough for this question"?2011-06-26
  • 0
    @Pete: I am right there with you.2011-06-26
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    @Pete: I've protected the question, as it's attracted a surprising number of brand-new users to chime in, but if someone makes the final vote to close, that would be fine as well. (Ideally, "protected" status would either have a higher reputation bar, or would be based on amount of time being an active member of the site, since it currently does not prevent answers from new users who have 101 points on math.SE via account association...)2011-06-26
  • 1
    This reminds me of “Chromatic Fantasy, And Feud” from Gödel, Escher, Bach.2011-06-26
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    @Agos: wow, it reminded me of one of the interstitial dialogues from *GEB* as well: I don't remember the name, but it must be the same one. Great minds...2011-06-26
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    I opened a [meta thread](http://meta.math.stackexchange.com/questions/2459/discussing-the-status-of-distance-from-0-to-1-is-equal-to-the-distance-from).2011-06-28
  • 57
    Ask him for his wallet, take out all the money. "You can't measure the distance between zero and 200."2011-06-28
  • 16
    You need a rhetorics stackexchange first, not a math one. He was mixing up different usages of numbers in everyday life. (First, he views numbers as "counting numbers" and then he allows to do measurement.)2011-06-28
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    "I am so upset that I want to punch him in the face" omg I nearly died laughing ^^2011-10-29
  • 0
    Your friend is merely pretending to be much pedantic. Pedanticism has no slot in mathematics. Suggest him to join Philosophy.2015-12-26

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