I have done that years ago already. I don't agree though. I'm not a parrot like you. — AgentTangarine

So years ago you looked it up, but still don't understand it now.

You don't agree with "it"? The continuum hypothesis? You have been claiming the continuum hypothesis for a zillion posts yet you say you don't agree with it! You are one really confused crank.

You are parroting your own world now as this is the second time you've said I am parroting, And even though I amply refuted that a while ago.

I can map N infinite times infinite times on R.

So years ago you looked it up, but still don't understand it now. — TonesInDeepFreeze

I don't mean that litteraly.

The only riddle you gave as an actual answer is that you can map N zero times on R. — AgentTangarine

So what? This is not a game with a scoreboard for how many questions I've answered.

Anyway, I've addressed TONS of your claims.

I don't mean that litteraly. — AgentTangarine

Then what do you mean? Why won't you now look up 'continuum hypothesis'?

So what? This is not a game with a scoreboard for how many questions I've answered. — TonesInDeepFreeze

Who says it is? I just said you have answered with a riddle.

I can map N infinite times infinite times on R. — AgentTangarine

Great. And I can make the sun disappear by wiggling my ears.

you have answered with a riddle. — AgentTangarine

The number 0 is not a riddle.

I looked it up when I wrote about the alephs, and it was even the reason for my post. Seems years ago.

The number 0 is not a riddle. — TonesInDeepFreeze

But if you say it's the number of times you can map it on R it is. I can even map a single element of N to R.

Yet you say you disagree with the continuum hypothesis now, while you have been claiming it in dozens and dozens of posts.

Yet you say you disagree with the continuum hypothesis now, while you have been claiming it in dozens and dozens of posts — TonesInDeepFreeze

So?

I can even map a single element of N to R. — AgentTangarine

Of course one can map a singleton set INTO R.

But there is no map of N ONTO R.

Of course one can map a singleton set INTO R.

But there is no map of N ONTO R — TonesInDeepFreeze

I can map a singleton on R too. No problem.

So you are in flat out contradiction with yourself.

So you are in flat out contradiction with yourself. — TonesInDeepFreeze

So?

I can map a singleton on R too. No problem. — AgentTangarine

Either you are insane or you don't know the meaning of 'map onto'.

So you are in flat out contradiction with yourself.
— TonesInDeepFreeze

So? — AgentTangarine

I think we have discovered a real infinity in life, which is what this post is about. You and me commenting on each other. I may be in flat contradiction with what I thought previously, that's right. But not with my present self. But for sure with you....

So which is it now? You claim that card(R) = aleph_1, thus asserting the continuum hypothesis? Or you deny that card(R) = aleph_1, thus denying the continuum hypothesis — TonesInDeepFreeze

No. I assert card(R)=aleph1.4. Call me crazy, like you wish. Card(RxR)=aleph2.6, more or less. 2^(1.4)=3, more or less, 2^(2.6)=6, more or less.

Then either you are insane or you don't know the meaning of 'map onto'. — TonesInDeepFreeze

I can send every cardinal on top of R. On top where I send it into.

So which is it now? You claim that card(R) = aleph_1, thus asserting the continuum hypothesis? Or you deny that card(R) = aleph_1, thus denying the continuum hypothesis?

Hardly matters though, since it is sheer crazy talk to say that there is a mapping of a singleton onto R.

I can send every cardinal on top of R. — AgentTangarine

As I said, you don't know the meaning of 'onto' in mathematics. Or you're insane.

"The mapping of 'f' is said to be onto if every element of Y is the f-image of at least one element of X."

Y=R, N=X...

This is the correspondence between infinite and infxinfxinf. And if r goes to 0.04566..., or 0.005667... or 0.000556654... (you get my point, I guess...) even infinite times are included. So the map becomes one between inf^2 and inf^4. Aleph1 and aleph2 — AgentTangarine

Are you off your meds again?

You guys need to get a hotel room. — jgill

Disgusting. — TonesInDeepFreeze

Pardon me, Ma'am. Here in the bunkhouse on the prairie I tend to forget there are ladies present. :worry:

Are you off your meds again? — jgill

I now even think R has cardinality aleph1.4!

You guys need to get a hotel room. — jgill

Haha! In Hilbert's hotel!

You guys need to get a hotel room. — TonesInDeepFreeze

Haha! In Hilbert's hotel! Wrong post...

EDIT:



That's not quite right since it has free variables on the right that aren't on the left.

f is onto Y if and only if (f is a function & range(f)= Y)

Note that that precludes Y from being a proper subset of range(f), which is a situation not usually mentioned. I suppose one could reformulate the definition to allow Y being a proper subset of the range(f) for a broader definition.

Also, some mathematicians consider a function to be not just the graph but also that the domain and the range are specified, and sometimes the domain and a co-domain (there may be different co-domains, since a co-domain can be any superset of the range). That could be made rigorous by saying a function is a triple <domain graph range> or alternatively <domain graph co-domain>. However, in set theory, the function is the graph, period, though of course that graph determines the domain and range.

That's not quite right or at best awkward, — TonesInDeepFreeze

I got it from the net...

Anyway, now you can see why there is no function f with a singleton domain an d onto R. — TonesInDeepFreeze

Still, I can map N onto R. Inf^3 times even...

R is onto Y if and only if (R is a relation & Az(zeY -> Ej <j z> e R)) — TonesInDeepFreeze

Huh?