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awarded  Nice Question
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Oct
9
comment Why is idempotence sufficient to be a projection?
@KevinCarlson It's not really about "the" definition, but about why.
Oct
7
comment Why is idempotence sufficient to be a projection?
@JHance I like that! Why is it dishonest? I think you are modeling the core issue nicely. If not pairs then there needs to be some extra structure to smooth out what I said.
Oct
7
comment Why is idempotence sufficient to be a projection?
@MartinR incidentally I only glanced at the Wikipedia definition. I was at a lee homology talk where $p \circ p=p$ was the definition of projection and was thinking back to that.
Oct
7
comment Why is idempotence sufficient to be a projection?
@MartinR but maybe the answer is the same: it isn't the idempotence that's sufficient, it's idempotence and endo-.
Oct
7
comment Why is idempotence sufficient to be a projection?
@MartinR thinking more of the categorical definition
Oct
7
asked Why is idempotence sufficient to be a projection?
Sep
27
revised Connecting physical tensors to mathematical tensors
edited body
Sep
27
comment Connecting physical tensors to mathematical tensors
@LeonardoFranciscoCavenaghi when I hear "trace" I think "counit". Is this in line with your thoughts?
Sep
27
asked Connecting physical tensors to mathematical tensors
Sep
22
comment Topological properties that the real line does not have
why on Earth was this so heavily downvoted?
Sep
20
comment Is there any intuitive understanding of normal subgroup?
Interesting. Does this extend to infinite-dimensional spaces, like let's say a change of numeraire in a time series?
Sep
17
comment Pen, pencils and paper to write math
I've also learned (from birdtracks.eu) that monochromacy and lack of diagrams are common for the printers convenience, not for the audience or for the writer. Frege's insistence on diagrams in the Begriffsschrift bankrupted him, and if you've tried to TeX a diagram you drew in 5 seconds, you know it's next to impossible. Organisation and clarity are great goals; aping typography (which is itself a stylisation of writing) is not. A few dashes of colour are great for high level organisation or to prevent drift into fraktur A vs sans serif A vs calligraphic A.
Sep
17
comment Pen, pencils and paper to write math
My life had become a lot better since I started writing in colours. I began doing this on a printout of Hatcher's K theory book. ("What is $p$ again?! And $T$ was defined … where??") Today I was doodling the reflection groups $A_2$ and … guess what … it's easier to read if $\to^{\alpha}$ and $\to^{\beta}$ are different colours.
Sep
17
comment Tangent to a line is the line itself. But, def. of tangent touches at 1 point?
This is a great question. I think I see where you're coming from, as "touches at a point" is the description usually given. But what you've come upon by yourself is a great reason not to define it that way! This is emblematic of a general pattern in mathematics and explains why definitions can sometimes appear convoluted: the simplest description needs to be edited for a few wrinkles ("let's not define 1 as prime", and many more).
Sep
15
asked ℂ version of alternating property