either way, i'm finding this thread highly entertaining and victorian. here is a gem -
No matter what I said to him, he just disregarded offhandedly. I am so upset that I want to punch him in the face, but I would rather get the proofs and show him that he is completely wrong. To me this would be the equivalent of slapping him on the face with a gauntlet
2) Define the complex number 1 (base 10) : http://us.metamath.org/mpegif/df-1.html (Note that the numbers 0 and 1 are constants defined as primitives of the complex number axiom system vs. the definition of the number 2 below)
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[ 2.9 ms ] story [ 15.3 ms ] threadThe real title of the question is: "I need mathematical proof that the distance from zero to 1 is the equal to the distance from 1 to 2"
No matter what I said to him, he just disregarded offhandedly. I am so upset that I want to punch him in the face, but I would rather get the proofs and show him that he is completely wrong. To me this would be the equivalent of slapping him on the face with a gauntlet
2) Define the complex number 1 (base 10) : http://us.metamath.org/mpegif/df-1.html (Note that the numbers 0 and 1 are constants defined as primitives of the complex number axiom system vs. the definition of the number 2 below)
3) 1 and 0 are distinct : http://us.metamath.org/mpegif/ax1ne0.html Axiom 14 of 25 for real and complex numbers (cf. http://us.metamath.org/mpegif/mmcomplex.html ), derived from ZF set theory (cf. http://us.metamath.org/mpegif/mmset.html#axioms ).
4) Define the unit interval with the Euclidean topology : http://us.metamath.org/mpegif/df-ii.html
5) 0 is an identity element for addition : http://us.metamath.org/mpegif/ax0id.html Axiom 15 of 25 for real and complex numbers (i.e. 0 + 1 = 1)
6) Define the number 2 as 2 = 1 + 1 : http://us.metamath.org/mpegif/df-2.html
QED