IIT and set theory

by sambarvada Tue Jul 12, 2011 10:57 pm

http://ckraju.net/blog/?cat=10

Sometime in early April I went to Ahmedabad to give a talk at the new IIT coming up there. One of those rare occasions when I missed my flight (even in Delhi, I didn’t anticipate a traffic jam at 5 a.m.), and so could reach only in the evening when the faculty were assembled for dinner.

One thing led to another, and soon there was a hot discussion going, on the validity and appropriateness of the current philosophy of mathematics.

I don’t like putting people down, but was pushed to do so, especially at the fag end of the day when my patience was short.

So, I publicly asked a senior faculty member whether he could define a set.

Of course he could not, and blustered that “a set is a collection of objects” (and then “a collection of well-defined objects”) which “definition” is complete nonsense. I did my best to suppress my laughter. (His junior was a little more knowledgeable and wondered whether it had something to do with Russell’s paradox.) The man was upset. The next day morning he asked me “do you think that I could have taught maths for 40 years, in IIT Bombay, if I did not know what a set is?” What was there for me to say: the facts spoke for themselves. He even added, that had I joined IIT Bombay, he would have taught me. I felt like saying “Thank God, I did not join”, but checked myself out of politeness.

===> What is wrong with the definition of a set being a collection of objects? Why is it complete nonsense?

by Kris Tue Jul 12, 2011 11:07 pm

Maybe he was hoping for the definition of a movie set? Smile

In seriousness, I have no idea why it is nonsense.

by Marathadi-Saamiyaar Wed Jul 13, 2011 12:04 am

sambarvada wrote:http://ckraju.net/blog/?cat=10

===> What is wrong with the definition of a set being a collection of objects? Why is it complete nonsense?

Georg Cantor, the founder of set theory, gave the following definition of a set at the beginning of his Beiträge zur Begründung der transfiniten Mengenlehre

A set is a gathering together into a whole of definite, distinct objects of our perception [Anschauung] and of our thought - which are called elements of the set.

by sambarvada Wed Jul 13, 2011 12:28 pm

Marathadi-Saamiyaar wrote:
sambarvada wrote:http://ckraju.net/blog/?cat=10

===> What is wrong with the definition of a set being a collection of objects? Why is it complete nonsense?

Georg Cantor, the founder of set theory, gave the following definition of a set at the beginning of his Beiträge zur Begründung der transfiniten Mengenlehre

A set is a gathering together into a whole of definite, distinct objects of our perception [Anschauung] and of our thought - which are called elements of the set.

===> C.K. Raju goes on to say in his article..

But what does it matter? IIT is a brand, right? Like Coca Cola or Pepsi. What product the brand produces, unhealthy sugar-water or whatever, is irrelevant. IIT is a brand, and we are all expected to prostrate ourselves before a brand. So what if the senior-most professors of mathematics at IIT don’t know even the starting point of the mathematics they teach. The important thing is that the government is behind them, for the people running the government, like the advisor to our prime minister, know even less mathematics, and therefore cannot judge who knows math and who does not, but simply go by brands. A perfect recipe for perpetual slavery.

Indians will have to fight for intellectual freedom.

by artood2 Thu Jul 14, 2011 1:08 pm

The silly old Indian notion of bookish definition being more important than the general understanding of principles. Why is the strict definition of such great importance? The general principles of set theory are simple and easily understood. Engineering is the application of scientific principle to build real life applications. The notion that anyone is technically incompetent because he does not say teh textbook definition of sets is absurd.

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