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| 2025-04-04 17:52:13 +0200 | <EvanR> | aaaddd < bbbccc |
| 2025-04-04 17:51:56 +0200 | amadaluzia | (~amadaluzi@user/amadaluzia) amadaluzia |
| 2025-04-04 17:51:38 +0200 | amadaluzia | (~amadaluzi@user/amadaluzia) (Ping timeout: 245 seconds) |
| 2025-04-04 17:51:32 +0200 | <EvanR> | nope |
| 2025-04-04 17:51:20 +0200 | <kuribas> | The formula? |
| 2025-04-04 17:51:14 +0200 | <EvanR> | what is |
| 2025-04-04 17:49:57 +0200 | <kuribas> | It's easy for naturals no? |
| 2025-04-04 17:49:35 +0200 | rit | (~rit@2409:40e0:39:317c:5ce4:875:e0a7:d628) |
| 2025-04-04 17:48:39 +0200 | lortabac | (~lortabac@2a01:e0a:541:b8f0:55ab:e185:7f81:54a4) (Ping timeout: 252 seconds) |
| 2025-04-04 17:47:19 +0200 | <EvanR> | immediately |
| 2025-04-04 17:46:49 +0200 | <kuribas> | Where do you get stuck? |
| 2025-04-04 17:46:35 +0200 | <EvanR> | oh this is the same question. Well I tried that too and couldn't figure it out |
| 2025-04-04 17:45:59 +0200 | <EvanR> | nvm |
| 2025-04-04 17:45:53 +0200 | <EvanR> | wait |
| 2025-04-04 17:45:50 +0200 | <EvanR> | just cancel 4 things? |
| 2025-04-04 17:45:39 +0200 | <EvanR> | if aaa / (bbb) < ccc / (ddd) then a/b < c/d? |
| 2025-04-04 17:43:30 +0200 | L29Ah | (~L29Ah@wikipedia/L29Ah) L29Ah |
| 2025-04-04 17:42:26 +0200 | L29Ah | (~L29Ah@wikipedia/L29Ah) (Ping timeout: 252 seconds) |
| 2025-04-04 17:41:52 +0200 | <kuribas> | For integral values of a, b, c, and d. |
| 2025-04-04 17:41:40 +0200 | <kuribas> | You could prove that (a*a*a)/(b*b*b) < (c*c*c*)/(d*d*d) then a/b < c/d |
| 2025-04-04 17:35:15 +0200 | <EvanR> | that means I don't have to solve this using the "hint use an indirect proof": Show that family of intervals [a,b] where a^3 <= 2 and 2 <= b^3 is consistent (any interval in the family intersects all the others) |
| 2025-04-04 17:32:39 +0200 | <EvanR> | cool |
| 2025-04-04 17:32:33 +0200 | <EvanR> | a < b? yes, then you're done. Or a == b, then a^3==b^3 contradicting a^3 < b^3. Or b < a, using the above, b^3 < a^3, also contradicting. |
| 2025-04-04 17:25:14 +0200 | <EvanR> | somehow |
| 2025-04-04 17:24:24 +0200 | <EvanR> | maybe in chapter 17 there will be a thing to prove that any monotonic functions on reals can be downgraded to a monotonic function on rationals |
| 2025-04-04 17:24:00 +0200 | fp1 | (~Thunderbi@2001:708:20:1406::1370) (Ping timeout: 272 seconds) |
| 2025-04-04 17:22:15 +0200 | <EvanR> | again, the task to is to reason from what's assumed and not from "any argument whatever" |
| 2025-04-04 17:21:51 +0200 | j1n37 | (~j1n37@user/j1n37) (Ping timeout: 276 seconds) |
| 2025-04-04 17:21:46 +0200 | <EvanR> | so I can't solve chapter 1 by using chapter 17 from the other book |
| 2025-04-04 17:21:38 +0200 | j1n37- | (~j1n37@user/j1n37) j1n37 |
| 2025-04-04 17:21:30 +0200 | <EvanR> | this is "real anaylsis: a constructive approach" |
| 2025-04-04 17:21:29 +0200 | <int-e> | (another fact) |
| 2025-04-04 17:21:10 +0200 | <int-e> | the rationals are a subfield of the reals |
| 2025-04-04 17:20:56 +0200 | <EvanR> | also it wouldn't even help, are you going to apply a function coded for real numbers to rationals? xD |
| 2025-04-04 17:20:28 +0200 | notdabs | (~Owner@2600:1700:69cf:9000:c0fa:b50a:3031:4dce) (Quit: Leaving) |
| 2025-04-04 17:20:04 +0200 | <EvanR> | I didn't that's the point |
| 2025-04-04 17:19:56 +0200 | <EvanR> | but we just proved that |
| 2025-04-04 17:19:56 +0200 | <int-e> | so how did you get there for the cube root in the reals? |
| 2025-04-04 17:19:36 +0200 | <EvanR> | it might be but I didn't get there |
| 2025-04-04 17:19:05 +0200 | int-e | shrugs |
| 2025-04-04 17:19:05 +0200 | <EvanR> | not absolute truths, or "doesn't matter somebody somewhere has already done this one" |
| 2025-04-04 17:18:58 +0200 | <int-e> | well, f(x) = x^3 being monotonic is a fact about rational number.s |
| 2025-04-04 17:18:32 +0200 | <EvanR> | I don't understand, I'm not skeptical. I'm trying to go from certain assumptions to a conclusion |
| 2025-04-04 17:16:47 +0200 | <int-e> | well it's not if you apply the same level of skepticism that you're currently applying to the strict monotonicity of f(x) = x^3 in the rationals |
| 2025-04-04 17:16:12 +0200 | <EvanR> | well that's a fact about real numbers right |
| 2025-04-04 17:16:08 +0200 | __jmcantrell__ | (~weechat@user/jmcantrell) jmcantrell |
| 2025-04-04 17:15:31 +0200 | <int-e> | TBH the funny part of this is that you were (apparently) willing to accept that the cube root function is strictly monotonic. |
| 2025-04-04 17:13:34 +0200 | dolio | (~dolio@130.44.140.168) dolio |
| 2025-04-04 17:13:18 +0200 | rit | (~rit@2409:40e0:39:317c:5ce4:875:e0a7:d628) (Remote host closed the connection) |
| 2025-04-04 17:13:03 +0200 | EvanR | recapitulates |