Turtle's troglodytes
Let me just remind you what these are: in his blog., Turtle asserted that, for any integer 
(where we may have, say 
) then 
.
Now I confess I haven't read the whole article, so for all I know this may have been covered, but the proof of this is laughably easy.
Take an integer like, oh I dunno, say
. Historically this notation means 
. So any integer can be written as 
.
It is true, almost by definition that
for any 
, so it follows immediately that
.
The very nice thing about this is that we see, also immediately, that, say
by commutativity and associativity of arithmetic addition.
(where we may have, say ) then . Now I confess I haven't read the whole article, so for all I know this may have been covered, but the proof of this is laughably easy.
Take an integer like, oh I dunno, say
. Historically this notation means . So any integer can be written as .It is true, almost by definition that
for any , so it follows immediately that.The very nice thing about this is that we see, also immediately, that, say
by commutativity and associativity of arithmetic addition.
Total Comments 1
Comments
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Thanks for reading as much as you did Ben.
Double thanks for the proof two...erhm...too. If you do read on, and it's a rather dauntingly long thread I admit, then we might get to some categorizng. 
I have a smaller spin-off thread that may give a quicker idea of some things I have done with these residues and obviously I hope it's something you have never seen. 
katabatak powers
Thanks again for bloggin' me.
Posted 05-13-2009 at 09:37 AM by Turtle
