Set Theory - Russell's Paradox: Oxford Mathematics 3rd Year Student Lecture

This is the second of four lectures from Robin Knight's 3rd Year Set Theory course. Robin writes:

"Infinity baffled mathematicians, and everyone else, for thousands of years. But around 1870, Georg Cantor worked out how to study infinity in a way that made sense, and created set theory. Modern mathematics can be built on set theory. These lectures begin to explore how".

You can watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists):

All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.

[notmyrealpseudonym]

If an axiom's identity was a 'similar' and not a 'same' would a logical consistency still be present? Similar has both same and difference in it and dually bound to it (it's an individual and undividable though looking like 2 things simultaneously, like a Nekker cube or a venn diagram for set theory).

[iwalk]

A very fascinating review of the latest tractor designs, I was particularly captivated by the presenters description of belt driven tractors and their implementation in industry. Splendid stuff!

[lepointique]

i have some questions if you can answer, it would help me immensely, first is consistent means that there is no theorem of the form Q and not(Q) for the set of axiomes?
second do we have the following implication (from goedel): if wa can prove that is consistent that its not ?.

[lepointique]

great video, i propose generally if U is a universe where we have objects (like sets for example), (we can also consider set instead of U) and we have a binary relation R then there is no object in U that satisfy [ for all object x xRy <=> not(xRx) ]or[ for all object x yRx <=> not(xRx)]

[s.m.zulfakarali]

🙏
Respected sir
Mostly important topic mathematics

[Clara-infu]

Congrats on the video, it was very nice :)

[chrisg]

Consider D = The set that includes now all and only those sets which did not include themselves previously. So if D includes itself now then it didn't include itself previously. But if it did include itself previously, then it doesn't now. Contradiction gone with the simple expedient of deciding on and making explicit the time order of the two set inclusion operations. Russell's paradox is no more paradoxical than any order of operations problem. Another example is 1 + 2 * 3, which also only needs a decision about which operation comes before the other, and signalling that order with some device like brackets.

[brendawilliams]

Why when in space is there is no direction? Everywhere is the same and you can’t prove anything but that you can’t prove anything. Step one looks dubious. Sets look dubious.