I omitted a detail in the previous toot for clarity. The definition of each of the above also gives the numeral representation. The number "one" has some additional technical definitions like "(number theory) the first positive natural number", but the main definition has no dots, does not refer to two, and actually seems to define one as the numeral 1...

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I wanted to know the etymology of the word "eleven" so looked it up on wiktionary. It seems to be something like "one left", but that's not as interesting as the definition: "the number after ten and before twelve"...!

The numbers down to five have a similar definition, although annoyingly not standardised, there seems to be a change in wording after ten.

Weirdly, three and four additionally represent the value with dots, and two *only* has the dots and doesn't mention one.

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Inspired by this toot: https://weirder.earth/@eldang/106268287486978878

(is there a way to "quote toot" in a reply to another toot?)

I noticed some weird behaviour on whatsapp (android). I just sent three messages with respectively 20, 30, 40 words to the same contact. The message boxes had different widths but multiple lines. When I go away and come back, they are all fixed width, but when I then scroll up and back down, the sizes are different again.

I know this is pretty trivial, but initially I just noticed the different sizes and wondered if there was in interesting reason. Now I'm very confused. Any ideas?

One idea I had: if you take a cycle and add a path between two of its vertices, you get a graph with three cycles. If you repeat, you either get six or seven depending on the choice of vertices. That means you can only achieve four or five cycles by gluing two graphs at a vertex, which I used to figure out a₄ and a₅.

a₅ is pretty hard to figure out by hand (I think the answer is 8) but it's easy to check that a₆=5 a₇=4.

A trivial upper bound on aₙ is 2n+1. I think there should be a not too difficult upper bound of O(√n).

Anyone know anything else?

Or have I got it wrong and 2m is the distance in America too? I'm sure I heard 6ft a lot when I was there last month...

Mathematician, computer scientist, bassist, knitter?

Joined Jan 2018