# Post about historical debate about numbers? May 31, 2014 8:04 AM Subscribe

I seem to recall a MetaFilter post (or comment in a related post?) that was about the historical debate over several mathematical issues, including a) whether 1 should be considered a number, and b) whether 1 is prime or composite. I searched for it, but can't find it. I recall there being a link to an academic paper about this topic, which is what I really want to find. Does anyone remember this?

[I know that the topic of the primality of .999.... can be a contentious topic. Let's keep it polite.]

[I know that the topic of the primality of .999.... can be a contentious topic. Let's keep it polite.]

And look at that, I was the first commenter on that post. That must be it, but I missed it in the search results. Thanks!

posted by Philosopher Dirtbike at 8:17 AM on May 31, 2014 [1 favorite]

posted by Philosopher Dirtbike at 8:17 AM on May 31, 2014 [1 favorite]

You navigated the vagaries of the metaqueue for this?

So, time to close this one up then?

I know, I know, not helping.

posted by cjorgensen at 11:21 AM on May 31, 2014 [1 favorite]

So, time to close this one up then?

I know, I know, not helping.

posted by cjorgensen at 11:21 AM on May 31, 2014 [1 favorite]

"What is the smallest prime?" was my post, and so was the .9999...=1 post. What can I say, I like to stir the mathematical shit.

posted by escabeche at 12:20 PM on May 31, 2014 [6 favorites]

posted by escabeche at 12:20 PM on May 31, 2014 [6 favorites]

*the mathematical shit*

What is known in elementary school as "the remainder".

posted by davidjmcgee at 1:30 PM on May 31, 2014 [4 favorites]

If anybody needs me, I'll be crafting my "What is 0^0?" FPP.

posted by escabeche at 2:03 PM on May 31, 2014 [4 favorites]

posted by escabeche at 2:03 PM on May 31, 2014 [4 favorites]

0^0 = ಠ_ಠ

posted by benito.strauss at 2:13 PM on May 31, 2014 [2 favorites]

posted by benito.strauss at 2:13 PM on May 31, 2014 [2 favorites]

If you're willing to accept a limit, then the limit as X approaches 0 of X^0 is 1.

And if you aren't, then you have to explain how differential calculus has gotten away all this time with division by zero.

posted by Chocolate Pickle at 2:53 PM on May 31, 2014

And if you aren't, then you have to explain how differential calculus has gotten away all this time with division by zero.

posted by Chocolate Pickle at 2:53 PM on May 31, 2014

"including a) whether 1 should be considered a number,"

posted by

Deep, very deep.

posted by marienbad at 2:55 PM on May 31, 2014

posted by

**Dirtbike***Philosopher*Deep, very deep.

posted by marienbad at 2:55 PM on May 31, 2014

*If you're willing to accept a limit,*

Sure, I'm willing to accept a limit. How do you feel about lim

_{x->0}(0

^{x})?

posted by Wolfdog at 5:23 PM on May 31, 2014 [2 favorites]

My calculator says that 0

I can ask it for the exact value of π, if anyone is interested.

posted by double block and bleed at 9:03 PM on May 31, 2014 [1 favorite]

^{0}is 1. So that settles it.I can ask it for the exact value of π, if anyone is interested.

posted by double block and bleed at 9:03 PM on May 31, 2014 [1 favorite]

*What can I say, I like to stir the mathematical shit.*

I scooped you on the 1+2+3+4... = -1/12 post tho

posted by empath at 12:14 AM on June 1, 2014

*You navigated the vagaries of the metaqueue for this?*

While submitting, I found that the submission form was bugged, so I provided an additional service!

posted by Philosopher Dirtbike at 6:32 AM on June 1, 2014

Yeah, but most importantly, |∅

posted by PMdixon at 12:15 PM on June 1, 2014

^{∅}|=1 (where ∅={}), so that settles it. ZFC QEDposted by PMdixon at 12:15 PM on June 1, 2014

*I scooped you on the 1+2+3+4... = -1/12 post tho*

Yeah but that's only because I have a whole section about my love for divergent series in my book, and I was actually forbidden by the publisher from writing about that stuff on the Internet in advance.

posted by escabeche at 4:36 PM on June 1, 2014

Is anyone else freaked out by the fact that 1 + 2 + 4 + 8 + 16 + ... would be the binary "number" ...11111, and has the value -1 (as if the binary "number" were two's complement)? What the fuck?!?!

posted by Jpfed at 5:13 AM on June 2, 2014

posted by Jpfed at 5:13 AM on June 2, 2014

To elaborate a bit, p-adic numbers have a prime base, and extend infinitely to the left.

In base 2:

....0000001 = 1, ...0000010=2, etc.

There's no special indication for negative numbers, neither are there decimal spaces.

So how do you get a negative number?

Well, you start with 0 and subtract 1, obviously:

Well, what, if you added 1 to it, would give you an infinite series of 0s?

The answer is an infinite series of 1s:

....11111111111:

It flips the first bit and then carries over to infinity.

Similarly, ...11111110 is -2, etc.

posted by empath at 6:58 AM on June 2, 2014 [1 favorite]

In base 2:

....0000001 = 1, ...0000010=2, etc.

There's no special indication for negative numbers, neither are there decimal spaces.

So how do you get a negative number?

Well, you start with 0 and subtract 1, obviously:

Well, what, if you added 1 to it, would give you an infinite series of 0s?

The answer is an infinite series of 1s:

....11111111111:

It flips the first bit and then carries over to infinity.

Similarly, ...11111110 is -2, etc.

posted by empath at 6:58 AM on June 2, 2014 [1 favorite]

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posted by dfan at 8:10 AM on May 31, 2014 [2 favorites]