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argonaut: A person who is engaged in a dangerous but potentially rewarding quest.


2d
comment Why only two binary operations?
OK. That comment helps me contextualise your answer; thanks.
2d
comment Why only two binary operations?
@PietroMajer Ah ok. Gotcha.
2d
comment Why only two binary operations?
Thanks Qiaochu. This is exactly the kind of answer I was hoping for. One question though, it seems like you're taking a 1-category as natural (in the first part). And maybe some other sort of object that doesn't naturally split into in/out is just as natural? (I only meant to give rings and cat 101 as examples.)
2d
comment Why only two binary operations?
@PietroMajer How do we know +,×,∘ are the only three interesting binary operations on $C(\mathbb{R},\mathbb{R})$?
2d
comment Why only two binary operations?
@NajibIdrissi Think about the amount of effort that goes into showing that the Cartesian product ("boring") satisfies a universal property. Is there some similar way of showing that it's "easy" to extend 2 to many ops?
2d
comment Why only two binary operations?
@NajibIdrissi OK, so for the second possible answer: (1) do we really know that? (2) how do we know that?
2d
comment Why only two binary operations?
@NajibIdrissi Yes. But I'd forgotten about them. Thanks.
2d
asked Why only two binary operations?
Oct
17
comment Is the theory of dual numbers strong enough to develop real analysis, and does it resemble Newton's historical method for doing calculus?
Do you really mean an order of magnitude smaller? $.001^2=.000001$ which is three orders of magnitude smaller.
Oct
17
comment How did Newton invent calculus before the construction of the real numbers?
I forget where I read this so I can't go back and check its veracity, so making this a comment. As far as I remember Newton actually worked quite a lot with infinitary series. If you think about this being a formal ring of functions, that really draws the focus away from the set over which the $x$'s are defined. This might be key to Newton's reasoning; if I find the source again I'll write a more thorough and verified answer.
Oct
4
revised Can I use my powers for good?
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Oct
3
answered Can I use my powers for good?
Oct
3
revised Intuition behind Matrix Multiplication
address another part of the question
Oct
3
answered Intuition behind Matrix Multiplication
Oct
3
answered Why is one “$\infty$” number enough for complex numbers?
Sep
30
revised What is the general area of mathematics to which this example belongs?
added 251 characters in body
Sep
30
answered What is a good book for learning math from the ground up?
Sep
25
answered Geometric visualization of covector?
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awarded  Autobiographer
Sep
24
answered undetstanding of Vectors, Tangent Vectors, Tangent Covectors