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so.. - Lograh — LiveJournal

Wednesday, 11.Feb.2004

18:03 - so..

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I'm going to sing the doom song now.
Doom doom doom doom
doom doom doom doom doom doom
doom doom doom
doom doom doom
doom doom doom doom doom doom doom doom doom doom. . .


So, we've all been introduced to those lovely numbers π (aprox 3.1415...) and e (aprox 2.71828...). They've been known of for hundreds, even thousands of years (the greeks knew of π, and I've heard (unconfirmed) rumour they knew of e as well). And it is known how they are trancendental numbers (not just irrational, but even more fun).

Pop quiz time!

What type of number is π+e.

It's a whole number! (like 3, 4, 5, etc...)
0(0.0%)
It's not a whole number, but not irrational (that is, it can be written as a fraction).
1(11.1%)
It's irrational (can't even be written as a fraction, like π and e themselves).
3(33.3%)
It's also trancendental.
1(11.1%)
It's an imaginary number (that'd be the ones with 'i' in them somewhere).
0(0.0%)
It's the type that makes my head hurt!
4(44.4%)


This poll brought on by my class discussion tonight where we touched on the proofs of the proper classifications of π and e (as examples of trancendental numbers over given rings -- so we diverged slightly).

Comments:

[User Picture]
From:pleckos
Date:19:19 11.Feb.2004 (UTC)
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You don't leave an option for tool!
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[User Picture]
From:lograh
Date:20:13 11.Feb.2004 (UTC)

Re:

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sorry, I *ahem* forgot that option. :)
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From:choasweasel
Date:21:21 11.Feb.2004 (UTC)

Hmmm.

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To guess off the top of my head, i would assume it remains irrational. I cannot see it becoming imaginary, it wont become whole, and i don't think it will be a fraction. I don't remember what trancedentals are, so thats out. And most certaintly does not hurt my head, i probably use those more than you do, but i am assuming that you actually do little calcutions using numerical values.
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[User Picture]
From:lograh
Date:7:41 12.Feb.2004 (UTC)

Re: Hmmm.

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sorry, I misspelt transcendental in my poll. damn.

here is a good explaination of what it means for a number to be transcendental. To sum up for those too lazy, though, a number is transcendental if it is not algebraic. A number is algebraic if it eventually becomes a rational number after taking it to a high enough power. For example, the square-root of 2, when squared, becomes a rational number (namely, 2). Thus the square-root of two is algebraic and thus not transcendental.

As for your claim that you may use them more than I, I shall point out that I'm in complex analysis right now. So unfortunately, odds are good that I'm using them more than you (both theoretically and computationally). Trust me, I look forward to the day you're using them more than me.
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