Is this a good argument

[Cratylus]

Theorem [MATH]\aleph_{0}[/MATH]<c

Proof

Let A=N,by Cantor’s Theorem if A<P(A) then |A|<|P(A)|. But |A|=[MATH]\aleph_{0}[/MATH] and |P(A)|=[MATH]2^{A}[/MATH][MATH]\longrightarrow[/MATH] |P(A)|=c

If [MATH]\aleph_{0}[/MATH] <[MATH]2^{A}[/MATH] then [MATH]\aleph_{0}[/MATH] <c

 

[pka]

On the page in this link read the second paragraph.

 

[Cratylus]

On the page in this link read the second paragraph.

I knew of the wiki already

 

[pka]

I knew of the wiki already

In that case why post the same proof and ask if it is valid?