

I need proof that zero to 1 is equal to 1 to 2 - mrcharles
http://math.stackexchange.com/questions/47714/i-need-mathematical-proof-that-the-distance-from-zero-to-1-is-the-equal-to-the-di

======
mazsa
1) Define the complex number 0 (base 10) :
<http://us.metamath.org/mpegif/df-0.html>

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

------
rudle
Grossly misleading headline.

The 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"

~~~
mrcharles
80 character limit makes it difficult to fit all that in.

~~~
rhizome
"I need a proof that the distances between '0 and 1' and '1 and 2' are equal"

------
wccrawford
Why in the world would you continue discourse with a troll?

~~~
bartl
"Troll" is the most abused word in internet forums.

