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Scary Math - Happy Halloween! - October 31, 2011
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Happy Scary Math Halloween mate... happy to be back on your site after quite a while.

In my head there was a voice reading the comic out loud with an inappropriate amount of scaryness.

Isn't M the largest simple group?
The largest sporadic simple group, if you're being pedantic. The largest known sporadic group, if you want to take pedantry to higher levels.

Alternatively, I might learn to read. Sorry!

While the definition you present for "Napier's Bones" is correct, the term is often used incorrectly for a slide rule. Indeed, for severakl years that was the only usage I was familiar with.

re: Supernatural Numbers

When did 0 (zero) become a natural number? It wasn't when I went to school; if it isn't this is an alternative to rather than a generalization of the naturals.

When I was at school, natural numbers were positive integers and whole numbers were non-negative integers, though wikipedia says there is no universal agreement on this. Still, I wonder what made you mention it. What is it about supernatural numbers that implies 0 is a natural number?

You need to allow n_p = 0, so 0 must be a natural number for the definition to make sense. But of course 0 is a natural number, and has been so at least since the times of Bourbaki. Natural numbers are used for counting, and 0 is the number of elements in the empty set!

I believe it has to do with the need to include 1 in the supernatural numbers. Since 1 is not prime, you're going to need to include p^0 in order to obtain 1 from the product. Therefore, since n sub(p) must be either a natural number or infinity, 0 must be a natural number in this definition.

Of course, that's just my guess...

Why is there a need to include 1 in the supernatural numbers?

the description of supernatural numbers states they are a generalization of the naturals, thus the naturals would be a subset of the supernaturals. 7 is a natural number; to represent 7 using the product given for the supernaturals p sub n must be 0 for all p except 7, but from the definition, this can only occur if 0 is either a natural or infinite. Note that the product form used in the definition implies that either 0 is not a natural (since it's not a supernatural) or 0 is a prime (which creates all sorts of other problems).

I still don't get it. You need 0 to be a natural so that you can include all the naturals in the supernaturals, but then since you included 0 in the naturals, and 0 can't be a supernatural as far as I can tell, you still don't include all the naturals in the supernaturals. So it doesn't work either way, and there's no indication of whether 0 is natural or not.

That's essentially my point -- the definition of supernatural needs to be modified. Two fairly obvious modifications are:
method 1) the exponents are each 0, a natural, or infinite.
method 2) all 0 a natural then make the supernaturals 0 or anything matching the definition as given.

Typo; the first word in method 2 should be call, not all.

method 3) Don't require that the Supernaturals be a superset of the naturals

In which case the supernaturals are an alternative to rather than a generalization of the naturals.

Wikipedia is correct. There is no universal agreement. Building number systems from Peano axioms is a bit easier, if you allow zero, but some authors don't. We universally agree to disagree on this, because it depends on the context which way is more convenient. When you open a new math book, this is on the list of facts that you should check early (and mention, if you are the author). The way I teach it is: "This a matter of faith. And in math we have freedom of religion. However, in this course, I am God."

I must say that, in the comments for most comics, Peano axioms rarely come up.

From my experience 0 is taught to not be a natural number in grade school and in lower level math classes in college. But higher level (graduate) classes will start including it because it is useful for certain theorems and proofs of theorems.

not enough fun.

Physics, on the other hand, has ghost fields and phantom dark energy.

Mathematics have the No Ghost Theorem.

Why isn't the Devil's curve in this list?

where are the spectral sequences?

You might also enjoy checking out the website of the US Metric Association, for ideas of how to teach and learn the SI Metric System, www.metric.org

As long as there is a kind of infinite confidence full of mind, again with strong will and independent of any intelligence, and one day will be successful.

Number of comments is directly porpotional to time :-)

No. But it is monotone increasing.

He should turn off comments on particularly old comments so we can say with certainty that it converges as well.

I thought comments tend to diverge over time.

Almost all integers are beasty numbers :)

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