Dennis Wildfogel first taught calculus over forty years ago. He received his Ph.D. from the University of California, Santa Barbara under the direction of Prof. Ky Fan.

In case you’ve seen my “How Big Is Infinity?” video, thought I’d tell you a bit about my personal connection to that topic. As mentioned in the video, I first heard about the idea of matching different infinite sets when I was in fourth grade. I certainly did not get it all then. As a senior in high school, I had a class that went through this material and I was gratified to finally be able to understand it. More amazingly, that summer, 1963, I read in the newspaper about Paul J. Cohen’s work, which had just been published – right after I had learned about this stuff (right up to but, of course, not including his work)! Then five years later, as a graduate student, I had a class from Prof. Cohen and had the good fortune of being able to speak with him on several occasions.

I just watched a video of yours titled “How Big Is Infinity?” here:

Your explanations are lucid and the animations are superb; it’s a great video.
Thousands of people are watching it, so I’d like to suggest a minor correction:

The question introduced at 6:14 is not the continuum hypothesis.
The set of reals and the power set of integers do have the same cardinality.
The continuum hypothesis is about the non-existence of a set that has larger cardinality than the set of integers but smaller than the set of reals.

You (and others who have pointed out the mistake) are quite right. I made a last minute change that led to the incorrect statement. I am working with the TED-Ed team today to get it fixed.

Hi Dennis,
Thanks for making this fantastic video!
A few years ago I made a sculpture entitled ‘The Hands of Cantor’, that used the Continuum Hypothesis as a jumping off point. After I first read about Georg Cantor and set theory, I had a dream that he had an infinite number of fingers on each hand. I became obsessed with creating a sculpture out of that dream. Here is a link to a short book I made about the project. You might be one of the few people that would actually get a kick out of it!

Hi Dennis, Thanks so much for this very interesting video. At 1:15 you mention that matching is a more fundamental operation than addition. Are there any other operations that are like matching in that respect? Are there operations more fundamental than matching?

Excellent video! This immediately reminded me of work I did last year on CDFs of continuous distributions. They never converged with the discrete CDFs and it is clear that the infinite real numbers are responsible for this divergence in areas.

I have put a copy of a working paper here ( http://www.ovvofinancialsystems.com/continuum.html ) illustrating how the analysis of a continuous uniform distribution generates the measurable extent to which the area of (infinite) rational numbers is less than that of (infinite) real numbers. There is no way to exclude the full set of real numbers through this analysis, thus supporting Cantor’s notion and the hypothesis. I would appreciate any comments, thanks.

Hello Dennis. I really enjoyed your video. I really enjoyed your presentation. You might be interested to know that mathematicians in Pisa are now developing new theories of transfinite number where the whole is always greater than the part and 1-1 correspondence. You might enjoy my paper on this, “Set Size and the Part-Whole Principle,” in the Review of Symbolic Logic. (Shorter, less formal version available for free on Scribd and PhilPapers.)

Also, I think I caught another error. I think Gödel proved that the Continuum Hypothesis is consistent with ZFC in 1940, not the 20s.

Hello Dennis. I really enjoyed your video. You might be interested to know that mathematicians in Pisa are now developing new theories of transfinite number where the whole is always greater than the part and 1-1 correspondence does not imply equal number. You might enjoy my paper on this, “Set Size and the Part-Whole Principle,” in the Review of Symbolic Logic. (Shorter, less formal version available for free on Scribd and PhilPapers.)

Also, I think I caught another error. I think Gödel proved that the Continuum Hypothesis is consistent with ZFC in 1940, not the 20s.

## 11 Comments

Hi Dennis,

I just watched a video of yours titled “How Big Is Infinity?” here:

Your explanations are lucid and the animations are superb; it’s a great video.

Thousands of people are watching it, so I’d like to suggest a minor correction:

The question introduced at 6:14 is not the continuum hypothesis.

The set of reals and the power set of integers do have the same cardinality.

The continuum hypothesis is about the non-existence of a set that has larger cardinality than the set of integers but smaller than the set of reals.

You (and others who have pointed out the mistake) are quite right. I made a last minute change that led to the incorrect statement. I am working with the TED-Ed team today to get it fixed.

Thanks for your comments!

Dennis

The video has been fixed. The link above now points to the corrected version. That corrected version is also on the TED-Ed website.

Hi Dennis,

Thanks for making this fantastic video!

A few years ago I made a sculpture entitled ‘The Hands of Cantor’, that used the Continuum Hypothesis as a jumping off point. After I first read about Georg Cantor and set theory, I had a dream that he had an infinite number of fingers on each hand. I became obsessed with creating a sculpture out of that dream. Here is a link to a short book I made about the project. You might be one of the few people that would actually get a kick out of it!

http://www.jamesmharrison.com/work/books/thehandsofcantor/index.html

I’d be happy to send you a hard copy if you would like one.

I’m really looking forward to viewing the rest of the Ted series with my son!

Best Wishes,

James Harrison

Sir,

Your video “How Big is Infinity” Boggles my mind.

It inspired me to write a Haiku:

Kings rule over kings

Infinity the concept

infinite itself

Best,

Rod J.

Hi Dennis, thanks for going out of your way to make the corrections. 🙂

Hi Dennis, Thanks so much for this very interesting video. At 1:15 you mention that matching is a more fundamental operation than addition. Are there any other operations that are like matching in that respect? Are there operations more fundamental than matching?

Hi Dennis,

Excellent video! This immediately reminded me of work I did last year on CDFs of continuous distributions. They never converged with the discrete CDFs and it is clear that the infinite real numbers are responsible for this divergence in areas.

I have put a copy of a working paper here ( http://www.ovvofinancialsystems.com/continuum.html ) illustrating how the analysis of a continuous uniform distribution generates the measurable extent to which the area of (infinite) rational numbers is less than that of (infinite) real numbers. There is no way to exclude the full set of real numbers through this analysis, thus supporting Cantor’s notion and the hypothesis. I would appreciate any comments, thanks.

Hello Dennis. I really enjoyed your video. I really enjoyed your presentation. You might be interested to know that mathematicians in Pisa are now developing new theories of transfinite number where the whole is always greater than the part and 1-1 correspondence. You might enjoy my paper on this, “Set Size and the Part-Whole Principle,” in the Review of Symbolic Logic. (Shorter, less formal version available for free on Scribd and PhilPapers.)

Also, I think I caught another error. I think Gödel proved that the Continuum Hypothesis is consistent with ZFC in 1940, not the 20s.

But great video all around.

Thanks for your comments, Matt! You are of course absolutely correct that Gödel’s result was published in 1940.

Hello Dennis. I really enjoyed your video. You might be interested to know that mathematicians in Pisa are now developing new theories of transfinite number where the whole is always greater than the part and 1-1 correspondence does not imply equal number. You might enjoy my paper on this, “Set Size and the Part-Whole Principle,” in the Review of Symbolic Logic. (Shorter, less formal version available for free on Scribd and PhilPapers.)

Also, I think I caught another error. I think Gödel proved that the Continuum Hypothesis is consistent with ZFC in 1940, not the 20s.

But great video all around.