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Sep
24
awarded  Autobiographer
Jun
6
awarded  Nice Question
Jun
6
awarded  Popular Question
Jul
16
awarded  Peer Pressure
Jul
16
awarded  Cleanup
Jun
7
revised Geometric Definitions: What is a straight line? What is a circle?
complete, more accurate answer
Jun
7
answered Geometric Definitions: What is a straight line? What is a circle?
Jun
7
comment Non-existence of irrational numbers?
It's a little bit like the question of whether the area of a surface is different when you bend it: Is the area larger on the convex side? One thinks of the surface as infinitely thin, but such a notion is useless for edge-cases like the above. If there isn't a difference, then there isn't even a notion of "curved surface".
Jun
7
comment Non-existence of irrational numbers?
Your example may not actually be perfectly correct. The issue involves the notion of a surface and what it means to "cut". You would require an beyond infinitely-sharp cutters, and they cannot be conceived. For this issue of irrational vs. indeterminate rational rests on the distinction of the real vs. idealism.
Jun
7
awarded  Supporter
Jun
7
comment How far can one get in analysis without leaving $\mathbb{Q}$?
See also "Is the diagonal of the unit square truly irrational?" for a geometric quasi-proof for the algebraist. There it's shown that it is not merely a notion of linguistics and terms.
Jun
7
comment Is a transcendental number necessarily irrational?
"Polynomials have precise definitions" is somewhat a matter of convention and habit. Beyond that there is only logical consistency. The question is whether these definitions stand in the light of new data. Please see the reference to geometry in the question "Is the diagonal of a square truly irrational?"
Jun
7
awarded  Commentator
Jun
7
comment Is a transcendental number necessarily irrational?
That doesn't look like a polynomial, only a "nomial". But this is where terminology becomes paramount. One can't argue on the grounds of reason here, because it involves definitions.
Jun
7
comment Is a transcendental number necessarily irrational?
Zero is not a root. Is it transcendental? I've started a little hullabaloo over at "Is the diagonal of a square truly irrational?" if you want to join in.
Dec
8
awarded  Scholar
Dec
8
revised Where does Feigenbaum's Constant (4.6692…) originate?
better wording
Dec
8
revised Where does Feigenbaum's Constant (4.6692…) originate?
deleted 7 characters in body
Sep
8
comment Where does Feigenbaum's Constant (4.6692…) originate?
@QiaochuYuan: Sorry was being sloppy, reworded. But, technically, dripping water probably can't -- at least at the place where it turns chaotic.
Sep
7
revised Where does Feigenbaum's Constant (4.6692…) originate?
better wording as main answer didn't seem to grok the idea of it