Newest at the top
| 2025-04-28 17:32:23 +0200 | <tomsmeding> | EvanR: 1/2^n is an integer multiple of 1/10^n: the multiple is 5^n, because 5^n * 1/10^n = (1/2)^n = 1/2^n |
| 2025-04-28 17:31:18 +0200 | <tomsmeding> | it does show where int-e's powers of 5 end up |
| 2025-04-28 17:31:14 +0200 | prdak | (~Thunderbi@user/prdak) (Read error: Connection reset by peer) |
| 2025-04-28 17:31:02 +0200 | <EvanR> | check it for n up to 10^900 and I'll start to be convinced (just kidding) |
| 2025-04-28 17:30:42 +0200 | <int-e> | [exa]: do you know the variant for binomial coefficients, https://en.wikipedia.org/wiki/Lucas%27s_theorem ? |
| 2025-04-28 17:30:25 +0200 | <tomsmeding> | anyway this checks the claim for 1 <= n <= 50 :p |
| 2025-04-28 17:30:23 +0200 | <EvanR> | fine I'll use paper |
| 2025-04-28 17:29:24 +0200 | <lambdabot> | Int -> CReal -> String |
| 2025-04-28 17:29:23 +0200 | <EvanR> | :t showCReal -- now with more unqualified |
| 2025-04-28 17:29:19 +0200 | <tomsmeding> | "dividing by powers of 2 is easy. Just exponentiate 5 and add some zeros" |
| 2025-04-28 17:28:36 +0200 | [exa] | reminded of that "zeros at the end of factorial" exercise |
| 2025-04-28 17:28:23 +0200 | <lambdabot> | True |
| 2025-04-28 17:28:22 +0200 | <tomsmeding> | > and [Data.Number.CReal.showCReal 80 (realToFrac (1 % 2^n)) == "0." ++ (let s = show (5^n) in replicate (n - length s) '0' ++ s) | n <- [1..50]] |
| 2025-04-28 17:27:44 +0200 | <int-e> | Same here. |
| 2025-04-28 17:27:35 +0200 | <EvanR> | I mean "if you understand it it's obvious" |
| 2025-04-28 17:26:35 +0200 | <int-e> | EvanR: Right. I mean it's not *quite* tautological... you may understand a complicated thing and it still won't be obvious. But this particular factoid isn't complicated. |
| 2025-04-28 17:26:13 +0200 | <tomsmeding> | these two numbers are alike |
| 2025-04-28 17:26:02 +0200 | <EvanR> | in decimal |
| 2025-04-28 17:26:00 +0200 | <lambdabot> | "0.00000095367431640625" |
| 2025-04-28 17:25:59 +0200 | <tomsmeding> | > Data.Number.CReal.showCReal (53 + 16) (realToFrac (1 % 2^20)) |
| 2025-04-28 17:25:58 +0200 | <EvanR> | k powers of 5 end in 5 |
| 2025-04-28 17:25:51 +0200 | <lambdabot> | • In the second argument of ‘showCReal’, namely ‘(1 % 2 ^ 20)’ |
| 2025-04-28 17:25:51 +0200 | <lambdabot> | • Couldn't match expected type ‘CReal’ with actual type ‘Ratio a0’ |
| 2025-04-28 17:25:51 +0200 | <lambdabot> | error: |
| 2025-04-28 17:25:49 +0200 | <tomsmeding> | > Data.Number.CReal.showCReal (53 + 16) (1 % 2^20) |
| 2025-04-28 17:25:39 +0200 | <EvanR> | tautology 37 |
| 2025-04-28 17:25:34 +0200 | <lambdabot> | 95367431640625 |
| 2025-04-28 17:25:33 +0200 | <tomsmeding> | > 5 ^ 20 |
| 2025-04-28 17:25:29 +0200 | <int-e> | once you understand it it will be obvious ;) |
| 2025-04-28 17:24:49 +0200 | <EvanR> | not obvious to me |
| 2025-04-28 17:24:35 +0200 | <EvanR> | but also a power of 5 |
| 2025-04-28 17:24:29 +0200 | <EvanR> | each time you multiply by 1/10 you get a nother power of two |
| 2025-04-28 17:24:26 +0200 | <int-e> | ;-) |
| 2025-04-28 17:24:24 +0200 | <int-e> | call me crazy, but I think that's actually true |
| 2025-04-28 17:24:15 +0200 | <int-e> | it's almost as if 1/2^n = 5^n/10^n |
| 2025-04-28 17:23:39 +0200 | <int-e> | (It worked, but I should be using 17.) |
| 2025-04-28 17:23:39 +0200 | acidjnk_new | (~acidjnk@p200300d6e71c4f61394430d048071491.dip0.t-ipconnect.de) (Ping timeout: 268 seconds) |
| 2025-04-28 17:23:18 +0200 | <tomsmeding> | Claim: if n >= 1 then the last digit is always 5. Claim: length of decimal expansion is n. Both admit a simple proof by induction :) |
| 2025-04-28 17:22:34 +0200 | <lambdabot> | "0.000010000000000000000818030539140313095458623138256371021270751953125" |
| 2025-04-28 17:22:33 +0200 | <int-e> | > Data.Number.CReal.showCReal (53 + 16) (realToFrac 0.00001) |
| 2025-04-28 17:22:24 +0200 | <EvanR> | o_O |
| 2025-04-28 17:22:20 +0200 | <EvanR> | you said decimal |
| 2025-04-28 17:22:20 +0200 | <tomsmeding> | and the number of _decimal_ digits is, too |
| 2025-04-28 17:22:17 +0200 | <lambdabot> | 16.609640474436812 |
| 2025-04-28 17:22:16 +0200 | <int-e> | > logBase 0.5 0.00001 |
| 2025-04-28 17:22:15 +0200 | <tomsmeding> | yes |
| 2025-04-28 17:22:09 +0200 | <EvanR> | the number of binary digits of 1/2^n is n, what were you talking about |
| 2025-04-28 17:21:59 +0200 | <int-e> | EvanR: so keeping track of that power of 2 tells you how many decimal digits you need |
| 2025-04-28 17:21:31 +0200 | <lambdabot> | "0.0000100000000000000008180305391403130954586231382563710212708" |
| 2025-04-28 17:21:30 +0200 | <EvanR> | > Data.Number.CReal.showCReal 61 (realToFrac 0.00001) |