Sme question about irrational numbers

In summary, the conversation discusses Cantor's second diagonal proof and how it shows that there are more irrational numbers than rational numbers. The cardinality of irrational numbers is shown to be 2^aleph_0, which is the same as the power of the continuum, or the cardinality of the real numbers. However, a question is raised about whether the set of all irrational numbers truly has the power of the continuum, as it is shown that sets of irrational numbers can be disjoint and still have the same cardinality. The conversation also includes examples using S1 and S2 to demonstrate this concept.
  • #71
aridno said:
This shows only that you have a "shadow" of intelligence.
Stop posting gibberish.
MAMA'MIA !

This is no more than an analogy.

Hurkyl,

Can you please explain to me why your advisors are so violent?

Why do you allow such a behavior?
 
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  • #72
If you want to speak maths, speak maths, not crappy analogies.
If you do that, and it isn't the first time, it will be pointed out to you. BLUNTLY.
 
  • #73
Violent? Oh, please, have you even read any sci.math?

Anyway, the simple explanation is that despite claiming that you wished to learn from professionals you've shown no absolutely no sign of doing so and have ignored our advice and just posted more of the same unmathematical musings.

For instance, to repeat myself yet again, why is the map f(s)=s defined for all s in some set S not a bijection? You have implied that it cannot be. Instead of answering this you went off on some bizarre tangent about "holds" which we find means "is true", though how a function "is true" is a mystery.


And as for your "number 4", the reals are expressed as limits of sequences of elements ni Q, so why isn't R countable? Using your "logic"?

There are several delicate areas of constructability and definability that (some) mathematicians care about. This isn't really getting close to it.
 
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  • #74
matt said:
Violent? Oh, please, have you even read any sci.math?
There is no moderator in sci.math.
If you want to speak maths, speak maths, not crappy analogies.
If you do that, and it isn't the first time, it will be pointed out to you. BLUNTLY.
I simply do not believe it. Hurkyl what is going on are you a moderator or not?
matt said:
And as for your "number 4", ...
What number 4, what are you talking about, Hurkyl why do you allow this madness?
 
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  • #75
Because yesterday there was a productive side discussion going on, and today I'm sick and was hoping I wouldn't have to deal with this. It's clear this isn't going anywhere now, though, so the decision is easy.
 
  • #76
For future reference, Tann was indeed another alias for Doron. His new alias has been banned, as will any more aliases he creates. Please let a mentor know if he pops up here again.

- Warren
 

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