Freethought & Rationalism Archive

Principia · 12-31-2002, 08:48 PM

To redeem myself, here's a proof. But to explain it without more than high school mathematics...

EDIT: here's another, more accessible proof, of the Schroeder-Bernstein Theorem.

Jayjay · 12-31-2002, 09:11 PM

Principia, you are redeemed.

That Schroeder-Bernstein theorem was pretty much what I was looking for.

Principia · 12-31-2002, 09:13 PM

I am curious, how did you come across the problem?

Jayjay · 12-31-2002, 09:59 PM

I am discussing the topic of countability in another message board. Mind wanders, and suddenly I wanted to have a minimalistic proof that "there exists a bijection from A to B" is equivalent to "there exists injections from A to B and vice versa", without referring to the concept of cardinality.

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12-31-2002, 08:48 PM	#11
Principia Veteran Member Join Date: Mar 2002 Location: anywhere Posts: 1,976	To redeem myself, here's a proof. But to explain it without more than high school mathematics... EDIT: here's another, more accessible proof, of the Schroeder-Bernstein Theorem.

12-31-2002, 09:11 PM	#12
Jayjay Veteran Member Join Date: Apr 2002 Location: Finland Posts: 6,261	Principia, you are redeemed. That Schroeder-Bernstein theorem was pretty much what I was looking for.

12-31-2002, 09:13 PM	#13
Principia Veteran Member Join Date: Mar 2002 Location: anywhere Posts: 1,976	I am curious, how did you come across the problem?

12-31-2002, 09:59 PM	#14
Jayjay Veteran Member Join Date: Apr 2002 Location: Finland Posts: 6,261	I am discussing the topic of countability in another message board. Mind wanders, and suddenly I wanted to have a minimalistic proof that "there exists a bijection from A to B" is equivalent to "there exists injections from A to B and vice versa", without referring to the concept of cardinality.

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