I got it from the net... — AgentTangarine
So? Not everything on the Internet is the sharpest formulation — TonesInDeepFreeze
f is onto Y if and only if (f is a function & range(f)= Y) — TonesInDeepFreeze
There you go what? I am the first to say that one has to use great caution trying to pick up math on the Internet. There are some excellent Internet sources, but usually the best approach is in books. I recommended the Internet to you only because I know you wouldn't bother to read a proper book on this subject. — TonesInDeepFreeze
There are a lot of good books indeed. — AgentTangarine
And you desperately need one if you are not to remain mired in your terrible confusions. — TonesInDeepFreeze
I don't take it too seriously — AgentTangarine
I can't see how R and RxR can have the same cardinality. — AgentTangarine
You could ask for more details about the proof mentioned by jgill and about the proof in the Quora thread. — TonesInDeepFreeze
It's making use of decimal expansions also but overlooks the majority of them. — AgentTangarine
I resist misinformation. — TonesInDeepFreeze
Name one. — TonesInDeepFreeze
conflating facts with opinions — Agent Smith
a number (x,y) — AgentTangarine
No way. One can offer alternative system; I enjoy reading about them. And one can even stipulate one's own terminology, and if it is rigorous, then we can accept it for purpose of discussion. But whether a proof is correct from given axioms is not a matter of opinion. Indeed, in principle, it is machine checkable. And the matter of what, in fact, mathematicians mean by the terminology is empirical fact, not opinion. — TonesInDeepFreeze
Rigor comes much, much later if I'm not mistaken. — Agent Smith
the definitions in math give me the impression that true understanding is being sacrificed for logical rigor. — Agent Smith
Take the square {(x,y):0<x<1,0<y<1} and map it one-to-one to the line {r:0<r<1) by using the procedure implied by the simple example (.329576914..., .925318623...) <-> .39229537168961243... — jgill
That is not a real number, you understand, right?
11m — TonesInDeepFreeze
Sounds good mr. Gill. Almost convincing. But you construct a new number from the both. Giving them both different decimal places. The diagonal proof of Cantor says you leave numbers out. Infinitely many. — AgentTangarine
Too, the definitions in math give me the impression that true understanding is being sacrificed for logical formalism. — Agent Smith
a number (x,y) say (0.678567, 0,98678) is contained in a single number 0.65456456. — AgentTangarine
The diagonal proof of Cantor says you leave numbers out. — AgentTangarine
You keep resorting to saying that I must consider the rest of what you posted. — TonesInDeepFreeze
It is the crank, not the mathematician who is dogmatic and exclusionary. — TonesInDeepFreeze
The diagonal proof shows that any map from N to R is not onto R. That is, there are real numbers not mapped to.
28m — TonesInDeepFreeze
Where did I do that? — AgentTangarine
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