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bio website pangaia.sourceforge.net
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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.


Mar
17
revised A question on transcendental numbers
added 30 characters in body
Mar
17
revised A question on transcendental numbers
added 33 characters in body
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"
Jan
12
comment A question on transcendental numbers
You claimed that transcendental numbers has a formal definition. I gave you the definition in Wikipedia. What is your definition?
Jan
12
comment A question on transcendental numbers
You didn't address my point: are you or are you not saying that transcendental numbers can be rational (since you claim it's well-defined).
Jan
12
comment A question on transcendental numbers
From wikipedia: "In mathematics, a transcendental number is a number that is not algebraic—that is, it is not a root of a non-zero polynomial equation with rational coefficients". But what is the root of x^2-4=0? A rational. So are you arguing that transcendental numbers can be rational?
Jan
12
revised A question on transcendental numbers
more precise word
Jan
12
answered A question on transcendental numbers
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.