Date: Apr 3, 2013 5:47 PM
Author: Virgil
Subject: Re: Matheology � 224
In article

<264f20e2-01d6-4e10-90cc-908a0532fd1c@y2g2000vbe.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> Can you prove by induction that the sum of the first m elements of

> your phantasy sets like 1, 1/2, 1/3, ... is m(m+1)/2? This is provable

> using induction.

Not outside of WOLKENMUEKENHEIM,

because it is false outside of WOLKENMUEKENHEIM!

For m = 1, 1 = 1(1+1)/2 is true

BUT for m = 2, 1 + 1/2 = 3/2

BUT 2(2+1)/2 = 3

AND for m = 3, 1 + 1/2 + 1/3 = 6/6 + 3/6 + 2/6 = 11/6

BUT 3(3+1)/2 = 12/2 = 6

Again notice the huge the difference between what WM claims is true

inside Wolkenmuekenheim and what is true outside of Wolkenmuekenheim.

It seems that inside Wolkenmuekenheim even the simplest of arithmetic

differs from that of standard mathematics.

Now if WM wants an inductive proof that the sum of the first m positive

integers equals m(m+1)/2....

initial step (m = 1) 1 = 1*(1+1)/2, true

Inductive step, assume 1+2+...+m = m*(m+1)/2

to prove 1+2+...+m + (m+1) = (m+1)((m+1)+1)/2

proof:

add (m+1) to both sides:

new LHS = 1+2+...+m + (m+1)

new RHS = m*(m+1)/2 + (m+1)

= (m+1)[m/2 + 1] distributive law,

AND m/2 + 1 = (m+2)/2 = ((m+1)+1)/2, SO

= (m+1)*((m+1)+1)/2 QED.

Thus by induction on N ={ 1,2,3,...},

the sum of the first m posItive integers is m(m+1)/2.

AND THAT IS THE SORT OF PROOF THAT WM IS APPARENTLY INCAPABLE OF

PRODUCING, AS HE NEVER PRODUCES ANYTHING LIKE IT.

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