What is the problem in this Proof

[Amer]

In your point of view what is the problem in this Proof
Claim any two natural a,b are equal
By induction
Let m= max{a,b}
if m=1 then a=b=1 since a,b natural
suppose it is hold for m=k
if
max{a,b} = k then a=b
test if
max{a,b} = k+1 , sub 1
max{a-1,b-1} = k which is the previous so a-1 = b-1 , a=b

I saw it in facebook

 

[Nono713]

In your point of view what is the problem in this Proof
Claim any two natural a,b are equal
By induction
Let m= max{a,b}
if m=1 then a=b=1 since a,b natural
suppose it is hold for m=k
if
max{a,b} = k then a=b
test if
max{a,b} = k+1 , sub 1
max{a-1,b-1} = k which is the previous so a-1 = b-1 , a=b

I saw it in facebook

I saw it on math.stackexchange too. The problem is that $\max{(a, b)} = k ~ \implies ~ a = b$ is clearly wrong, and the proof was designed to hide this fact. For instance, $\max{(5, 7)} = 7$, but last time I checked we had $5 \ne 7$.

In essence, this "proof" doesn't show that all natural numbers are equal, it shows that any two equal natural numbers are equal ;)​

 

[Evgeny.Makarov]

The problem is that $\max{(a, b)} = k ~ \implies ~ a = b$ is clearly wrong, and the proof was designed to hide this fact. For instance, $\max{(5, 7)} = 7$, but last time I checked we had $5 \ne 7$.

But this does not explain which proof step in particular is wrong. Of course the implication max(a, b) = k ⇒ a = b is false, just like the original claim that a = b for all a, b. But the proof claims to show just that, and the question is where the mistake in the proof is located.

 

[caffeinemachine]

In your point of view what is the problem in this Proof
Claim any two natural a,b are equal
By induction
Let m= max{a,b}
if m=1 then a=b=1 since a,b natural
suppose it is hold for m=k
if
max{a,b} = k then a=b
test if
max{a,b} = k+1 , sub 1
max{a-1,b-1} = k which is the previous so a-1 = b-1 , a=b

I saw it in facebook

The proof goes wrong in the last two sentences.

We have max{a,b}=k+1

Now we have max{a-1,b-1}=k.

We now want to apply the induction hypothesis here to have a-1=b-1 and thus a=b. But we can't do this. This is because we are not sure if a-1 and b-1 are natural numbers. We can very well have one of a-1 and b-1 equal to 0.

So this is the problem in the proof.

 

[blue_raver22]

The problem with this proof is that it is incomplete and lacks a clear explanation of the steps taken. It also does not provide any supporting evidence or mathematical principles to back up the claim. Additionally, the use of informal language and referencing to a source on Facebook raises doubts about the credibility of the proof. Overall, this proof lacks rigor and does not follow the standard conventions of mathematical proofs.