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Personally I find these definitions a bit circular. Equations like "a + x = b", "ax = b" and "sin(x) = 0" have no meaning unless you have an understanding of w
by Aicy 5y ago
Personally I find these definitions a bit circular.
Equations like "a + x = b", "ax = b" and "sin(x) = 0" have no meaning unless you have an understanding of what the terms mean, or could mean.
- Gehinnn 5y agoYou can easily define + on natural numbers and * on integer numbers without running into problems! Thus there is no cirularity here.
- deleted 5y ago[deleted]
- Aicy 5y agoI understand very well that the peano axioms for example are logical and not circular. My point was that I think your explanation relies on the experience on what a number is, having used those equations before with the terms actually representing real numbers (such as 3 + 2 = 5 instead of a + x = b and sin(180) = 0 instead of sin(x) = 0). So as a definition of what a number is it's circular as you presume experience with numbers and what they mean.