How to pronounce “cantor” in English

Cantor had revealed something remarkable.

Cantor's results rocked the mathematical community.

Cantor had successfully well ordered a set that was infinite in both directions, but it was only countably infinite.

Cantor was a devout Lutheran and he believed God was speaking through him.

Cantor dreamed of joining him at the University of Berlin, but all his applications were mysteriously denied.

Cantor was so relieved.

Cantor's developments, except he couldn't quite push it all the way through and ended up throwing up his hands in confusion

Cantor did a wonderful thing in the decade-- Georg Cantor, famous German mathematician-- did a wonderful thing in the decade from 1870 to 1880.

Cantor actually copied the usual way of counting, starting at one.

Cantor carried on, imagining counting an infinite collection, getting to the end, and then you have a problem of what the next number is after all the finite whole numbers.

Cantor eventually-- well, he was institutionalized several times and died in a lunatic asylum in Halle, which later became

Cantor. This is the the place where he went to meet Cantor.

Cantora developed and signed a handful of bands, hundreds of concerts, and eventually raised a technology fund where we were helping startups and their founders navigate the music industry.

Georg Cantor was a talented German mathematician who found himself at the center of a firestorm after publishing one of his very first papers

So Cantor called these countable infinities, but then there are bigger infinities, Cantor called them uncountable.

What Cantor called a well-order.

Well Cantor realized he could just pick zero as the starting point and from there his ordering went one, negative one, two,

So Cantor took the rejection personally.

Soon Cantor suffered what would be the first of many nervous breakdowns.

Once Cantor was released from the sanatorium, he stepped away from math, a broken man.

So Cantor's well-ordering theorem and Zermelo's axiom of choice are equivalent.

And Cantor originally called it infinity, but it doesn't behave like the infinity that people know from calculus.

But Cantor said in this paper in the 1940s-- Godel.

Kronecker completely dismissed Cantor's work, labeling him a scientific charlatan and a corrupter of the youth.

Zermelo realized Cantor's assumption needed to be formalized into something that holds up in a system of proof.

- Back to Cantor's argument.

was controversial in Cantor's day more than 100 years ago, but I think it's most commonly looked at today as, you know, one of the

following different anthropomorphization of Cantor's argument.

They also include Cantor's infinite ordinal numbers, which are not very familiar to people.

So with Cantor, omega plus 1, omega plus 2, dot, dot, dot, omega plus n typically, and then omega plus omega, which is omega times 2.

I wondered whether Cantor had had similar feelings.

And what Cantor did is he reinvented, for all practical purposes, mathematics.

But what Cantor did is he said, let's take a seed and let's plant a seed.

That's why this is called Cantor's Diagonalization Proof and it shows there must be more real numbers between zero and one than there are natural numbers extending out

but there was one big reason that Cantor was so confident in his theorem.

And Kronecker used to be Cantor's teacher.

In the audience was not only Cantor but also his wife, two of his daughters and his colleagues.

shall cast us from the paradise that Cantor has created for us."

So I came into Murray Cantor's talk with that in mind and I said, Murray, is it flow and resistance?

He worked for a company called Cantor Fitzgerald, which lost all 658 of their employees.

Zermelo's breakthrough came when he discovered something profound in Cantor's work, a mechanism which Cantor uses unconsciously and instinctively everywhere,

- Okay, so Cantor wants to prove that the infinity of the real numbers is different and strictly larger than the infinity of the natural numbers.

controversy that occurs in connection with this observation about whether Cantor's construction is constructive or not.

They're wonderful things, Cantor's ordinal numbers.

Assuming he now has a complete infinite list, Cantor writes down another real number and to do it, he takes the first digit of the first number

The leading German mathematician Kronecker called Cantor a corrupter of youth and tried to block his career.

The tension between the Cantor-Hume principle and what could be called Euclid's principle, which is that the whole is always greater than the part, is a principle that Euclid

Given a list of numbers, Cantor gives us a specific means of constructing a real number that's not on the list, is a

So we talked about Cantor's proof that the real numbers, the set of real numbers is an uncountable infinity,