3 votes

Understanding inductive proof of $\sum_{{m=k}}^{N} {m\choose k} = {N+1\choose K+1}$

Can someone please help me understand how the argument of mathematical induction serves to prove this identity? There is no such thing as a step 2 separate from step 3. In ordinary induction, the ...
Julio Di Egidio's user avatar
1 vote

Understanding inductive proof of $\sum_{{m=k}}^{N} {m\choose k} = {N+1\choose K+1}$

Seems to me that your confusion comes in the ideia of the inducion in itself, and not from this particular proof. Hence, I wil try to clarify the way you should think induction. The first step in a ...
peE_'s user avatar
  • 49
1 vote

Characterizing congruences on the algebra of natural numbers

I don't know why I didn't realize I could also get to $R$ using $[z,s]$. Starting at $1+R$ and going both ways around the squares, I get: $$\text{succ}(\pi_1(n,m))=\text{succ}(n)=n+1=\pi_1([z,s](n,m))$...
msb15's user avatar
  • 126
1 vote

Is this proof for mathematical induction valid?

Let's work in Intuitionistic ZF, a constructive (as usually understood today) version of set theory. But, instead of the normal infinity axiom, suppose we have $ℝ$ and the other constants used in your ...
Dan Doel's user avatar
  • 3,868

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