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by snowwindwaves
4565 days ago
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Along a similar vein you may also enjoy http://arxiv.org/pdf/1303.6576 The foundations of analysis by Larry Clifton. I always enjoy checking out the references in his papers as they are often hundreds of years old or more. |
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This is a curious paper. It's a rigorous derivation of (positive) real numbers without the use of 0 or negative numbers anywhere. It isn't very useful, although the fact that this can easily be done is by itself interesting.
I have sometimes thought about the possibility of us encountering an advanced alien civilization and trying to match our math to theirs. Someone told me recently that if aliens were able to get into space, we can take it for granted that they knew negative numbers (in addition to more advanced concepts). I disagreed. Negative numbers are very convenient, but all the math that's needed for modern physics can, I think, be built up without them in a way that's more bulky and awkward, but not an order of magnitude bulky. This paper is weak evidence of my position.