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The Remarkable Number 1/89 (2004)

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Re: The Remarkable Number 1/89 (2004)

#91

Post by jessaustin »

gnulinux wrote: post #83
grahamlee wrote: post #63

Earlier quoted context omitted.

No number is unremarkable. Let's construct the set of all unremarkable numbers. Now, let's construct the sequence of those numbers in order. The first member of that sequence has the remarkable property that it is the smallest unremarkable number. That is remarkable, so remove it from the set. By induction, the set must be empty.

That doesn't work because real numbers are not enumerable, so you cannot induce over them. That joke "proof" only works for natural numbers and goes like this: Theorem: all natural numbers are interesting * Base case: 0 is interesting because it is the smallest natural number, as well as the identity element of + operation. * Inductive case: Assume the theorem holds for all m, m By induction, we conclude all natural…

...only works for natural numbers...

That proof also works for the rationals with a suitable ordering. Example: 0, 1, -1, 2, -2, 1/2, -1/2, 3, -3, 1/3, -1/3, 2/3, etc....

Re: The Remarkable Number 1/89 (2004)

#92

Post by Stupulous »

Stupulous wrote: post #90
zekrioca wrote: post #50

Earlier quoted context omitted.

Then it is also silly to (erroneously) mention who discovered such a property, don't you think?

The proof follows from this instance of the discovery, with an Oklahoma U student indepently discovering and an OU professor indepently proving . I think that's a perfectly reasonable way to track what happened. I am unable to open the pdf or follow any of the links from the wiki talk page, so the proof may predate this instance, which would invalidate my point.

Sorry, can't edit the comment from here, those italics make it seem snarky. Should have been an asterisk after proving and before the next sentece that I forgot to escape.

Re: The Remarkable Number 1/89 (2004)

#93

Post by gnulinux »

jessaustin wrote: post #91
gnulinux wrote: post #83

Earlier quoted context omitted.

That doesn't work because real numbers are not enumerable, so you cannot induce over them. That joke "proof" only works for natural numbers and goes like this: Theorem: all natural numbers are interesting * Base case: 0 is interesting because it is the smallest natural number, as well as the identity element of + operation. * Inductive case: Assume the theorem holds for all m, m By induction, we conclude all natural…

...only works for natural numbers... That proof also works for the rationals with a suitable ordering. Example: 0, 1, -1, 2, -2, 1/2, -1/2, 3, -3, 1/3, -1/3, 2/3, etc....

Yes works for all enumerable set (i.e. all sets that have a bijection with natural numbers).

Re: The Remarkable Number 1/89 (2004)

#94

Post by carapace »

alisonkisk wrote: post #23
wumms wrote: post #11

From an archived talk (2011) on wikipedia [0]: "The linked page misleadingly suggests that a certain Cody Birsner discovered the relationship between the series and the fraction, whereas it had been known for a considerable time before". Günter Köhler, 1983 (published in the The Fibonacci Quarterly, 1985; who cites earlier papers from 1977 and 1981): https://www.fq.math.ca/Scanned/23-1/kohler.pdf [0] https://en.wikip…

It's a bit silly to chase down original authorship of an idea that is a minor detail visible to many people who work in a field. It's like asking who was the first person to discover that all multiples of 11 have the same parity in the respective sums of their odd and even digits.

Making a discovery in mathematics confers a kind of immortality. You're part of a conversation that has lasted centuries and will continue for the life of mankind.

Re: The Remarkable Number 1/89 (2004)

#96

Post by wiml »

chrismorgan wrote: post #49
NickHoff wrote: post #39

Earlier quoted context omitted.

I've always liked 1/7 as well, and I never realized that thing about doubling from 7 giving 14, 28, 56. People are always impressed when I can rattle off the digits of x/7. By the way, I appreciate your use of U+0305 combining overline. Did you enter those manually or do you have some neat way of doing it?

Heh, last time I spouted about 1⁄7 here someone asked about the overline too: https://news.ycombinator.com/item?id=24302104 . I love my Compose key.

I've had my CapsLock bound to Compose for ages; it's a great use of that piece of keyboard realestate.

I still don't have a good way to discover compose sequences other than by groveling through xkb and compose files. I really wish there were a character-palette tool that would tell me how to type the characters by introspecting the current input settings.

Re: The Remarkable Number 1/89 (2004)

#98

Post by galaxyLogic »

jerf wrote: post #19
burlesona wrote: post #2

Okay, as a non-mathematician, I see something like this and I think... “neat coincidence?” But the world of numbers seems to be full of these neat coincidences. So do any of the math folks here have a theory or explanation of why ?

Imagine the real number line is a database that you can run SELECT queries against, and you don't have to worry about giving a computational procedure that produces the result, it just magically gets produced. Now, imagine you write a query, like, say, "SELECT number WHERE number = .01 * FIB[1] + .001 * FIB[2] + .0001 * FIB[3]" and so on until you get what the article discusses. It isn't necessarily that surprising t…

There are many co-incidences that seem to be so strange that you start thinking they can not be co-incidences, until you take into account that there are an infinite number of facts which do not seem to be co-incidental at all. But beware of untrue facts: https://en.wikipedia.org/wiki/Lincoln%E2%80%93Kennedy_coinci...

Re: The Remarkable Number 1/89 (2004)

#99

Post by mypalmike »

NextHendrix wrote: post #95
pessimizer wrote: post #56

Earlier quoted context omitted.

I use CapsLock; lowest usefulness to size ratio possible.

Caps lock is much more useful as a home row ctrl key

Why stop there though? Mine is configured to be ESC when tapped, CTRL when held down. Took a while to get used to, but it's a big improvement compared to other ways of handling ESC on a 60% keyboard.

Re: The Remarkable Number 1/89 (2004)

#100

Post by Jtsummers »

ehsankia wrote: post #78
wumms wrote: post #11

From an archived talk (2011) on wikipedia [0]: "The linked page misleadingly suggests that a certain Cody Birsner discovered the relationship between the series and the fraction, whereas it had been known for a considerable time before". Günter Köhler, 1983 (published in the The Fibonacci Quarterly, 1985; who cites earlier papers from 1977 and 1981): https://www.fq.math.ca/Scanned/23-1/kohler.pdf [0] https://en.wikip…

It tickles me that there was a "Fibonacci Quarterly" where people shared their favorite new Fibonacci facts on a quarterly basis.

Not was, is. I was curious about that as well.

https://www.fq.math.ca/list-of-issues.html

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