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#2 2012-11-07 18:53:11
- bob bundy
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Re: Induction Proofs
hi hempy,
The following site has an explanation of proof by induction. The final example is the proof for the geometric sequence. The notation is a little different but you should be able to 'convert it'.
http://www.csee.umbc.edu/~stephens/203/PDF/4-2.pdf
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#3 2012-11-08 18:22:40
- noelevans
- Full Member
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Re: Induction Proofs
Hi!
Suppose that a is a constant and r is not zero or one and for each n in {1,2,3,...}
0
n
a = r*a . Show that a = a * r for each n in {1,2,3,...}.
n n-1 n 0
1
For n=1 we have a = r*a = r*a = a *1 . So it works for n=1.
1 1-1 0 0
Now suppose that for some positive integer k,
k k k k+1
we have a = a *r . Then a = r*a = r*a = r*a *r = a * r * r = a*r
k 0 k+1 (k+1)-1 k 0 0 0
So given that it works for k we have shown that it works for k+1, which is the inductions step.
Therefore it works for all n in {1,2,3,...}.
Is there any way to put this page into a half-space mode? Then the super and subscripts would
look pretty nice. 
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.
#4 2012-11-08 19:21:42
- bob bundy
- Moderator
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Re: Induction Proofs
hi noelevans
You could try Latex:
http://www.mathisfunforum.com/viewtopic.php?id=4397
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#5 2012-11-09 00:33:33
- anonimnystefy
- Real Member
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Re: Induction Proofs
The forum also has built in tags which allows use of subscripts and superscripts withouth knowledge of latex:
For example an.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#6 2012-11-09 03:47:16
- bobbym
- Administrator
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Re: Induction Proofs
Hi noelevans;
Give this a try:
http://latex.codecogs.com/editor.php
perfect latex everytime!
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#8 2012-11-09 07:25:50
- anonimnystefy
- Real Member
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Re: Induction Proofs
Pretty math?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#9 2012-11-09 12:29:58
- noelevans
- Full Member
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Re: Induction Proofs
LaTex input (not so pretty) vs LaTex output = Pretty math
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.