Question for atheists...
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28-03-2016, 06:46 PM
RE: Question for atheists...
(28-03-2016 05:48 PM)GirlyMan Wrote:  Cantor's diagonalization and Hilbert's Hotel are some of the most elegant examples of proof by contradiction.

Hilbert's Hotel is not a proof by contradiction. It's a demonstration of the non-intuitiveness of infinities.

Quote:But I think there is a group of mathematicians called constructivists (I think) who reject proof by contradiction. Yes? Dunno whether they are fringe or manistream

Neither, but they are a minority.

Quote:or just creepy like Chas.

Dodgy

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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28-03-2016, 07:22 PM
RE: Question for atheists...
Why is this thread still alive?

"Owl," said Rabbit shortly, "you and I have brains. The others have fluff. If there is any thinking to be done in this Forest - and when I say thinking I mean thinking - you and I must do it."
- A. A. Milne, The House at Pooh Corner
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28-03-2016, 07:25 PM
RE: Question for atheists...
(28-03-2016 06:46 PM)Chas Wrote:  
(28-03-2016 05:48 PM)GirlyMan Wrote:  Cantor's diagonalization and Hilbert's Hotel are some of the most elegant examples of proof by contradiction.

Hilbert's Hotel is not a proof by contradiction. It's a demonstration of the non-intuitiveness of infinities.

It assumes a bijection and then demonstrates there is none. Is that not a proof by contradiction?

#sigh
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28-03-2016, 07:27 PM
RE: Question for atheists...
(28-03-2016 07:22 PM)Unbeliever Wrote:  Why is this thread still alive?

Because "reasons"

Weeping
Dodgy


But as if to knock me down, reality came around
And without so much as a mere touch, cut me into little pieces

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28-03-2016, 07:48 PM
RE: Question for atheists...
(28-03-2016 07:25 PM)GirlyMan Wrote:  
(28-03-2016 06:46 PM)Chas Wrote:  Hilbert's Hotel is not a proof by contradiction. It's a demonstration of the non-intuitiveness of infinities.

It assumes a bijection and then demonstrates there is none. Is that not a proof by contradiction?

It does no such thing.

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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28-03-2016, 07:51 PM
RE: Question for atheists...
(28-03-2016 07:25 PM)GirlyMan Wrote:  It assumes a bijection and then demonstrates there is none. Is that not a proof by contradiction?

Doctor gave me a bijection once. I don't recommend it. Drinking Beverage

But now I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth.

~ Umberto Eco
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28-03-2016, 08:01 PM
RE: Question for atheists...
(28-03-2016 07:48 PM)Chas Wrote:  
(28-03-2016 07:25 PM)GirlyMan Wrote:  It assumes a bijection and then demonstrates there is none. Is that not a proof by contradiction?

It does no such thing.

It most certainly does.

#sigh
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28-03-2016, 08:12 PM
RE: Question for atheists...
(28-03-2016 07:51 PM)evenheathen Wrote:  
(28-03-2016 07:25 PM)GirlyMan Wrote:  It assumes a bijection and then demonstrates there is none. Is that not a proof by contradiction?

Doctor gave me a bijection once. I don't recommend it. Drinking Beverage

I had one too. Consider
A bijection ...
That may explain everything. Dodgy

Insufferable know-it-all.Einstein God has a plan for us. Please stop screwing it up with your prayers.
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28-03-2016, 08:25 PM
RE: Question for atheists...
(28-03-2016 08:01 PM)GirlyMan Wrote:  
(28-03-2016 07:48 PM)Chas Wrote:  It does no such thing.

It most certainly does.

No it dose not

pascal wager in a nut shell

god essentially wants a army of cowardly slaves who love it out of a selfish desire not to be punished and avoid said punishment by ideological luck
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28-03-2016, 08:43 PM
RE: Question for atheists...
(28-03-2016 08:01 PM)GirlyMan Wrote:  
(28-03-2016 07:48 PM)Chas Wrote:  It does no such thing.

It most certainly does.

Demonstrate it.

Hint: "Rephrased, for any countably infinite set, there exists a bijective function which maps the countably infinite set to the set of natural numbers, even if the countably infinite set contains the natural numbers. For example, the set of rational numbers—those numbers which can be written as a quotient of integers—contains the natural numbers as a subset, but is no bigger than the set of natural numbers since the rationals are countable: there is a bijection from the naturals to the rationals."

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