I'm losing my favourite game
Dec. 15th, 2004 09:42 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
ventaReturn of an old rant:
I just called the Swan to book my car in for some work on Saturday. During my fifteen second conversation with the receptionist, she said "just bear with me a second" three times.
That's a whopping 12 bwm/minute, on average.
I just called the Swan to book my car in for some work on Saturday. During my fifteen second conversation with the receptionist, she said "just bear with me a second" three times.
That's a whopping 12 bwm/minute, on average.
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Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-15 03:08 am (UTC)Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-15 03:13 am (UTC)0/x = 0, regardless of the value of x.
x/0 = infinity, regardless of the value of x.
Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-15 03:48 am (UTC)0/x = 0 only for x != 0.
x/0 is undefined, not infinite.
Proof:
* Let Z be some well-defined extension to the integers ('infinity') such that x/0 = Z.
* 1/0 = Z = 2/0
* 1/0 = 2/0 => 1 = 2 (contradiction)
Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-15 05:14 am (UTC)Yes, my statement wasn't very rigorous. And by simple substitution it showed that, if x=0, then in mathematical terminology, you're knackered.
Are you allowed to write "= infinity" in a proof ? (I know I did above, but that was because I was scribbling something intended to be short form for lots of things with -> and epsiolins).
Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-15 05:37 am (UTC)Only if it's clear which well-defined thing you mean.
Assuming (like all grown up mathematicians) that we do everything with set theory, then any particular 'infinity' is just a member of the set you're doing proofs in. The tricky part is deciding which set that is and then making sure every step of the proof is valid in the set in question.
Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-15 05:40 am (UTC)A while back I was forced to give in and admit that topoi are probably grown up, even though I don't understand them.
Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-15 05:46 pm (UTC)Can we send them scaffolding poles to shore up the edges just in case?
Re: I see I'm not the only person who likes silly ratios.
Date: 2005-02-02 11:22 pm (UTC)Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-15 06:05 am (UTC)Let Z be a multiplicative inverse for 0. Then 0*Z = 1. But 0*Z = 0 by, like, the first theorem we ever proved about fields, which is that 0*anything is 0.
You've only showed that in a field x/0 can't be constant for all x. This shows that furthermore, x/0 isn't defined for any x.
Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-15 05:13 pm (UTC)Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-16 03:04 am (UTC)Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-15 05:44 am (UTC)f(x)=infinity when x=y is a common mathematician laziness, which really means
f(x) tends to infinity as x tends to y. Clearly, the original statement cannot be true, as it's simply not legitimate to write "= infinity" in a proof.
Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-15 04:29 am (UTC)( X + infinity ) / N
where X is the usual Pope density, and N is "some time period"
= infinity
Not 20.404!
Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-15 05:55 am (UTC)0/x is always 0
x/x is always 1
x/0 is always infinite.
Therefore it is a common belief that 0/0 can be either 0, 1 or infinite.
As others have said, these premises are not true when you are dividing by zero.
Re: I see I'm not the only person who likes silly ratios.
Date: 2004-12-16 03:04 am (UTC)