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/sci/ - Science & Math

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3868619 No.3868619 [Reply] [Original]

OK guys, here's a question that's been stumping me for the last few days, I'm gonna keep cracking at it but let me know if you have any suggestions.

If we let the 26 symbols in the English alphabet represent the 26 numbers in base 26 (i.e. A=0, B=1, C=2,...) PROVE that .MMMMMMMMM..... is equal to the decimal number 0.8. (so that's an infinite sequence of Ms). So of course this an infinite sequence of "12s" as it where. If you calculate it you can get arbitrarily close to 0.8 (using 12 over consecutive negative powers of 26), but the problem I'm having is proving that it equals this. Obviously it will require some analysis. Any ideas?

>> No.3868640

N =/= .MMMMMMMMM...

>> No.3868646

well yes N =/= .MMMMMMMM...., but I don't see your point? That wasn't my question.

>> No.3868652

Where are you getting 0.8?
I can show that it's equal to 0.48 with a simple geometric series.

>> No.3868654

In base k, the expression 0.nnnnnn... will equal to n / (k - 1).

In this case, 0.MMMMM... will equal 12 / 25, or about 0.48

>> No.3868664

>>3868654
Accordingly, the expression you're looking for is 4 / 5, or 20 / 25, in other words, 0.UUUUU....

>> No.3868670

>will equal 12 / 25, or about 0.48
>12/25
>about 0.48
>about
>implying that 12/25 isn't exactly equal to 0.48

>> No.3868672

<span class="math">\sum_{j=1}^{\infty}12\cdot\left(\frac{1}{26}\right)^j =12\left(\sum_{j=0}^{\infty}\left(\frac{1}{26}\right)^j-1 \right )[/spoiler]

Google geometric series

>> No.3868681

>>3868670
> implying nearness excludes equality

>> No.3868686

>>3868681
>implying that "about" doesn't imply uncertainty
>implying you would say "100 cents is about a dollar"
>implying that doesn't make you sound pants-on-head retarded
>implying that you think you can backpedal
>confirmed for retard

>> No.3868691
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3868691

>>3868686
> still implying that nearness excludes equality

>> No.3868708

hmmmm... I should have know this would degenerate into an argument, oh well. I've got it now, I was wrong in my assumption that it was 0.8, it is in fact .48 (not about .48, but exactly). From there it's easy to prove that you get arbitrarily close to .48, thanks guys, don't get too contentious....

>> No.3868718

>>3868691
>implying that because all squares are rectangles, all rectangles are squares

keep trolling, nigger

iaintevenmadlol.jpg

>> No.3868729

>>3868718
> implying that statement is related to anything posted in this thread and not some deluded non-sequitur

>> No.3868768

>>3868729
not sure if troll or retard

"x is exactly y" gives more information than "x is about y", the same way that "x is a square" gives more information than "x is a rectangle". In the later case, x might be a square or it might not.

You're whole fucking argument is that ambiguity is the same thing as certainty. Saying that 12/25 is about 0.48 and saying that it is exactly 0.48 do not convey the same information.

So yeah, troll or retard.

inb4 "trolled u", still not mad

>> No.3868772

>>3868768
your


fuck

>> No.3868781

>>3868768
> You're whole fucking argument is that ambiguity is the same thing as certainty. Saying that 12/25 is about 0.48 and saying that it is exactly 0.48 do not convey the same information.

> implying anybody claimed that
> implying the discussion was ever, at any point, that nearness is equivalent to equality
> implying you specifically didn't say that if 12/25 is near 0.48, then 12/25 is not 0.48
>> 3868670

>> No.3868796

>>3868781
> implying you specifically didn't say that if 12/25 is near 0.48, then 12/25 is not 0.48
>>3868670

English obviously isn't your native language. Saying that "12/25 is about 0.48" implies that you're not certain that it is exactly 0.48. It directly means that you do not know the exact value, only an approximate value. That's how "about" is used in the English language. At no point did I claim that it excluded the possibility, only that it showed uncertainty where there should be none.