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Emerged from the singularity, now understand where Euler's equation comes from. Help me implement the Unified Information Model at pangaia.sourceforge.net. See the wikiwikiweb at c2.com.

Please forgive the lack of using TeX formatting for math equations. I have no idea how to do it.


Jul
13
revised Is the diagonal of the unit square truly irrational?
clarified grammar
Jul
13
revised Is the diagonal of the unit square truly irrational?
deleted 5 characters in body
Jun
6
awarded  Nice Question
Jun
6
awarded  Popular Question
Apr
29
revised Is the diagonal of the unit square truly irrational?
made it more clear, language
Jan
19
revised Is the diagonal of the unit square truly irrational?
deleted 195 characters in body
Jan
13
comment Is the diagonal of the unit square truly irrational?
@MJD; that is a very astute comparison, I think.
Jan
13
revised Is the diagonal of the unit square truly irrational?
changed to term used on ward's wiki "UnknowableNumber"
Jul
16
awarded  Peer Pressure
Jul
16
awarded  Cleanup
Jun
7
comment Is the diagonal of the unit square truly irrational?
I will tell you that I think the field has been conflating various domains that have only recently come to light. One of the main ones is the Platonic domain of geometry with the purely quantized realm of rationals. Think about how one can logicially and consistently interchange between a semi-discrete domain with a continuous domain of geometry and you'll see where the sqrt(2) lies at the boundary of both. I'm looking for collaborators to elucidate some of this.
Jun
7
comment Is the diagonal of the unit square truly irrational?
I'm going to guess that you're equivocating with the word "is"/"are" and the symbol "=" (more specifically, your use of "are" in the first sentence). You can't always use them interchangeably. Question on definitions: Is 2i (of the complex domain) an "even" number?
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
revised Is the diagonal of the unit square truly irrational?
emphasis