Bits of Learning

Learning sometimes happens in big jumps, but mostly in little tiny steps. I share my baby steps of learning here, mostly on topics around programming, programming languages, software engineering, and computing in general. But occasionally, even on other disciplines of engineering or even science. I mostly learn through examples and doing. And this place is a logbook of my experiences in learning something. You may find several things interesting here: little cute snippets of (hopefully useful) code, a bit of backing theory, and a lot of gyan on how learning can be so much fun.

Friday, February 10, 2006

Set Containing All Sets

Can there be a set containing all sets? No!

Seems it's a well-known theorem in set theory, but frankly, didn't seem intuitive in the beginning. I didn't know that any such theorem is there. However, on giving some serious thought, I hit upon many proofs, all of course based on some common line of thought.

That basic thing is: All sets have their power sets. Period.

OK! More directly it always means that given a set we can always compute a set which is bigger than itself. That is its power-set. A set containing all sets is the biggest possible set. But then, its power-set is bigger than it.

Hence proved!
Quite nice.

1 comment:

Ajit said...

You want to read Hofstadter if you haven't yet, that is.