How to pronounce “zermelo” in English

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

Zermelo uses the axiom of choice to choose a number from the set of all real numbers.

Zermelo had proved the well-ordering theorem and well ordered the real numbers all in under a month.

Zermelo took something mathematicians had unknowingly relied on for decades and turned it into a formal axiom.

Zermelo scanned dozens of papers from other mathematicians and realized they had also been using the axiom all along, even those who had criticized Cantor's work.

Zermelo's proof didn't actually construct a well order.

Zermelo's. And it's fascinating also because the axiom of choice was widely regarded as a kind of, you know, basic principle at first,

Ernst Zermelo. Zermelo was a German mathematician who had recently developed a keen interest in Cantor's work and as he listened to König's presentation,

As Zermelo indexes each number with the natural numbers, at first it might seem like he'd run into a problem because the natural numbers are only accountably infinite,

- Right - ...Zermelo-Fraenkel set theory, that's the Z and the F and the C in that is this...

the Zermelo set theory and gave the proof that in that theory, you can prove that every set admits a well ordering.

early 20th century with Zermelo's idea. I mean, the history is quite fascinating because Zermelo in 1904 offered a proof

forms of- of Zermelo-Fraenkel set theory and so on.

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

this was a case when Zermelo seemed to be, from principles that seemed quite reasonable, proving this obvious untruth.

now, and Zermelo didn't either.

Within 24 hours, Zermelo had pinpointed the problem.

- I read some historical accounts by historians about that time period, specifically about Zermelo's axioms and his proof of the well-order theorem.

But then Zermelo and others actually looked into the mathematical papers and so on of some of the people who had been

So, I mean, the history of the current set theory axioms, known as the Zermelo-Fraenkel axioms, came out in the

—that he was pressed to produce the theory in which his argument could be formalized, and that was the origin of what's known as Zermelo set theory.

So cone of perplexity, ZFC, or Zermelo-Fraenkel set theory with the Axiom of Choice, as we mentioned, is the standard foundation for most

So, Zermelo introduced most of these axioms, I mean, as part of what's now called Zermelo set