Multiplication -- prove this one by induction

[rb120134]

Homework Statement

Prove by induction that for any natural numbers n and m , n x (m++)= (n x m) + n

Relevant Equations

n x (m++) = (n x m) +n

Prove by induction that for any natural numbers n and m , n x (m++)= (n x m) + n

The base case, n=0 gives 0 x m++=(0 x m) +0 gives 0=0
Now assume n x (m++) = (n x m) +n
For n++ we get

n++(m++)=((n++)m) + n++

from this point I am stuck, how can I prove both sides are the same?

 

[PAllen]

What do you mean by m++ ? In mathematics, this means nothing. Do you mean the programming language C convention? But then, actually n * (m++) == n *m is true, while n * (++m) == n * m + n is true.

 

[Mark44]

What do you mean by m++ ? In mathematics, this means nothing. Do you mean the programming language C convention? But then, actually n * (m++) == n *m is true, while n * (++m) == n * m + n is true.

The OP posted a similar question using this notation in another thread (https://www.physicsforums.com/threads/proof-multiplication-is-commutative.782057/#post-6537515).

I believe it is less sophisticated notation than is used in C et al, and has nothing to do with pre- or post-increment. I believe that the notation m++ is just shorthand for m + 1.

 

[PAllen]

The OP posted a similar question using this notation in another thread (https://www.physicsforums.com/threads/proof-multiplication-is-commutative.782057/#post-6537515).

I believe it is less sophisticated notation than is used in C et al, and has nothing to do with pre- or post-increment. I believe that the notation m++ is just shorthand for m + 1.

shorthand in what way? Same number of characters, and + needs right pinky reach as well as left pinky shift, while 1 just needs left pinky reach (at least on my keyboard).

 

[Mark44]

shorthand in what way?

OK, maybe samehand...

 

[PAllen]

Can you say what axioms you are allowed to use? I would also recommend explicitly writing + 1 to better use normal arithmetic axioms.