Talk:2966: Exam Numbers - Revision history

ISaveXKCDpapers at 13:59, 3 August 2024

2024-08-03T13:59:11Z

172.70.206.158 at 13:58, 3 August 2024

2024-08-03T13:58:33Z

172.70.206.159: added comment

2024-08-03T13:57:42Z

added comment

172.69.195.175 at 08:48, 3 August 2024

2024-08-03T08:48:50Z

172.71.142.174: /* What is a number? */ revise

2024-08-03T05:51:25Z

‎What is a number?: revise

172.70.214.124: comment

2024-08-03T05:50:04Z

comment

172.69.23.49: Adding comment about infinite numbers

2024-08-03T03:12:38Z

Adding comment about infinite numbers

172.69.246.142: haiii hi haiiiii hiiii haii :333c

2024-08-02T21:43:05Z

haiii hi haiiiii hiiii haii :333c

108.162.238.68 at 18:59, 2 August 2024

2024-08-02T18:59:34Z

141.101.99.172 at 10:43, 2 August 2024

2024-08-02T10:43:26Z

@@ Line 43: / Line 43: @@
 :The answer
 :: (-2x sin(2x)+cos(2x)-2x)/28 + C
-:is indeed incorrect. However, your reasoning for thinking this is wrong. Two functions can have the same derivative while also having different outputs for the same input. For example, sin^2(x) and -cos^2(x) have the same derivative, but sin^2(0) = 0, whereas -cos^2(0) = -1. [[Special:Contributions/172.70.206.158|172.70.206.158]] 13:58, 3 August 2024 (UTC)
+:is indeed incorrect. However, your reasoning for thinking this is wrong. Two functions can have the same derivative while also having different outputs for the same input. For example, sin^2(x) and -cos^2(x) have the same derivative, but sin^2(0) = 0, whereas -cos^2(0) = -1. [[User:ISaveXKCDpapers|ISaveXKCDpapers]] ([[User talk:ISaveXKCDpapers|talk]]) 13:59, 3 August 2024 (UTC)
 As to '''biggest numbers:''' I thought most people would say the answers revolved around "nine-stuffing." For a kindergartener, stuff in as many bare <code>9</code>s as possible. For a postgrad, mix in exponentiation and write your numbers even smaller than a kindergartener can. <code>9^9^9^9...</code> or perhaps <code>99^99^99...</code> or…I'm not sure what's optimal. Of course, I'm not math postdoc ;) Or maybe some integrals or big-∏ notation. [[User:JohnHawkinson|JohnHawkinson]] ([[User talk:JohnHawkinson|talk]]) 12:41, 1 August 2024 (UTC)

@@ Line 43: / Line 43: @@
 :The answer
 :: (-2x sin(2x)+cos(2x)-2x)/28 + C
-:is indeed incorrect. However, your reasoning for thinking this is wrong. Two functions can have the same derivative while also having different outputs for the same input. For example, sin^2(x) and -cos^2(x) have the same derivative, but sin^2(0) = 0, whereas -cos^2(0) = -1.
+:is indeed incorrect. However, your reasoning for thinking this is wrong. Two functions can have the same derivative while also having different outputs for the same input. For example, sin^2(x) and -cos^2(x) have the same derivative, but sin^2(0) = 0, whereas -cos^2(0) = -1. [[Special:Contributions/172.70.206.158|172.70.206.158]] 13:58, 3 August 2024 (UTC)
 As to '''biggest numbers:''' I thought most people would say the answers revolved around "nine-stuffing." For a kindergartener, stuff in as many bare <code>9</code>s as possible. For a postgrad, mix in exponentiation and write your numbers even smaller than a kindergartener can. <code>9^9^9^9...</code> or perhaps <code>99^99^99...</code> or…I'm not sure what's optimal. Of course, I'm not math postdoc ;) Or maybe some integrals or big-∏ notation. [[User:JohnHawkinson|JohnHawkinson]] ([[User talk:JohnHawkinson|talk]]) 12:41, 1 August 2024 (UTC)

@@ Line 40: / Line 40: @@
 :but they messed up the places of the negation and square.
 :Though the important part here isn't what it is at any f(x), but what it is for any f(x)-f(y). In this particular case, f(pi)-f(0). [[Special:Contributions/162.158.41.121|162.158.41.121]] 04:49, 1 August 2024 (UTC)
 As to '''biggest numbers:''' I thought most people would say the answers revolved around "nine-stuffing." For a kindergartener, stuff in as many bare <code>9</code>s as possible. For a postgrad, mix in exponentiation and write your numbers even smaller than a kindergartener can. <code>9^9^9^9...</code> or perhaps <code>99^99^99...</code> or…I'm not sure what's optimal. Of course, I'm not math postdoc ;) Or maybe some integrals or big-∏ notation. [[User:JohnHawkinson|JohnHawkinson]] ([[User talk:JohnHawkinson|talk]]) 12:41, 1 August 2024 (UTC)

@@ Line 88: / Line 88: @@
 :All right, all right. I yield. That’s some... _impressive_ reasoning. If we are going to redefine words to meaninglessness then there is no hope of engaging in useful discussion. I’m sure Randall will at least get a good laugh out of the idea that post-grad math students would submit “infinity” as the largest number they could think of. I still think it a disservice to readers to posit infinity as a _valid_ answer, though. [[User:Dúthomhas|Dúthomhas]] ([[User talk:Dúthomhas|talk]]) 05:05, 1 August 2024 (UTC)
 ::This isn't redefining words to meaninglessness. Do you know how many branches of math there are that generalize the concept of "number"? 2500 years ago the Greeks didn't believe irrational numbers were numbers (and Hippasus supposedly drowned for discovering them), and it was a long time before 0 was accepted as a number, but now we have entire hierarchies of numbers. 100 years ago Georg Cantor created another upheaval in mathematics when he invented Set theory along with the infinite ordinals and cardinals, which are usually referred to as "numbers". Complex analysis defines the "extended complex numbers", modeled by the [https://en.wikipedia.org/wiki/Riemann_sphere Riemann sphere], which includes a "point at infinity" (and of course you can [https://en.wikipedia.org/wiki/Projectively_extended_real_line extend the real numbers]] similarly). Non-standard analysis defines not only infinite but infinitesimal numbers as [https://en.wikipedia.org/wiki/Hyperreal_number Hyperreal number]s. Granted, I'll agree that using "infitity" without any qualification or context is not really precise enough to do anything useful with. [[Special:Contributions/172.69.23.49|172.69.23.49]] 03:12, 3 August 2024 (UTC)
 Y'all, the answer is clearly 1.  Sincerely, someone who has studied probability.[[Special:Contributions/162.158.137.155|162.158.137.155]] 14:04, 1 August 2024 (UTC)

← Older revision		Revision as of 05:51, 3 August 2024
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	:The ''true'' Cosmic cosmologist surely knows that H<sub>0</sub> is 1 (exactly and always), redefining all subsequently derived units in terms of that and the other 'true constants' of the universe... ;) [[Special:Contributions/141.101.99.172\|141.101.99.172]] 10:43, 2 August 2024 (UTC)		:The ''true'' Cosmic cosmologist surely knows that H<sub>0</sub> is 1 (exactly and always), redefining all subsequently derived units in terms of that and the other 'true constants' of the universe... ;) [[Special:Contributions/141.101.99.172\|141.101.99.172]] 10:43, 2 August 2024 (UTC)

−	Infinity comes up in kindergarten more often than most people think. Kids learn to keep asking "why?" in sequence around four, and they don't stop until they get an answer which makes them face some terrifying ~~question~~, usually ~~around~~ mortality. Infinity is small potatoes and involved in the answer to a suprising number of simple math questions. [[Special:Contributions/172.70.214.124\|172.70.214.124]] 05:50, 3 August 2024 (UTC)	+	Infinity comes up in kindergarten more often than most people think. Kids learn to keep asking "why?" in sequence around four, and they don't stop until they get an answer which makes them face some terrifying reality, usually concerning mortality. Infinity is small potatoes and involved in the answer to a suprising number of simple math questions. [[Special:Contributions/172.70.214.124\|172.70.214.124]] 05:50, 3 August 2024 (UTC)

← Older revision		Revision as of 05:50, 3 August 2024
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	No actual cosmologist denotes the Hubble constant in Hz. It's about 70 (km/s)/Mpc. [[Special:Contributions/162.158.41.22\|162.158.41.22]] 04:23, 2 August 2024 (UTC)		No actual cosmologist denotes the Hubble constant in Hz. It's about 70 (km/s)/Mpc. [[Special:Contributions/162.158.41.22\|162.158.41.22]] 04:23, 2 August 2024 (UTC)
	:The ''true'' Cosmic cosmologist surely knows that H<sub>0</sub> is 1 (exactly and always), redefining all subsequently derived units in terms of that and the other 'true constants' of the universe... ;) [[Special:Contributions/141.101.99.172\|141.101.99.172]] 10:43, 2 August 2024 (UTC)		:The ''true'' Cosmic cosmologist surely knows that H<sub>0</sub> is 1 (exactly and always), redefining all subsequently derived units in terms of that and the other 'true constants' of the universe... ;) [[Special:Contributions/141.101.99.172\|141.101.99.172]] 10:43, 2 August 2024 (UTC)
		+
		+	Infinity comes up in kindergarten more often than most people think. Kids learn to keep asking "why?" in sequence around four, and they don't stop until they get an answer which makes them face some terrifying question, usually around mortality. Infinity is small potatoes and involved in the answer to a suprising number of simple math questions. [[Special:Contributions/172.70.214.124\|172.70.214.124]] 05:50, 3 August 2024 (UTC)

← Older revision		Revision as of 03:12, 3 August 2024
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	:All right, all right. I yield. That’s some... _impressive_ reasoning. If we are going to redefine words to meaninglessness then there is no hope of engaging in useful discussion. I’m sure Randall will at least get a good laugh out of the idea that post-grad math students would submit “infinity” as the largest number they could think of. I still think it a disservice to readers to posit infinity as a _valid_ answer, though. [[User:Dúthomhas\|Dúthomhas]] ([[User talk:Dúthomhas\|talk]]) 05:05, 1 August 2024 (UTC)		:All right, all right. I yield. That’s some... _impressive_ reasoning. If we are going to redefine words to meaninglessness then there is no hope of engaging in useful discussion. I’m sure Randall will at least get a good laugh out of the idea that post-grad math students would submit “infinity” as the largest number they could think of. I still think it a disservice to readers to posit infinity as a _valid_ answer, though. [[User:Dúthomhas\|Dúthomhas]] ([[User talk:Dúthomhas\|talk]]) 05:05, 1 August 2024 (UTC)
		+	::This isn't redefining words to meaninglessness. Do you know how many branches of math there are that generalize the concept of "number"? 2500 years ago the Greeks didn't believe irrational numbers were numbers (and Hippasus supposedly drowned for discovering them), and it was a long time before 0 was accepted as a number, but now we have entire hierarchies of numbers. 100 years ago Georg Cantor created another upheaval in mathematics when he invented Set theory along with the infinite ordinals and cardinals, which are usually referred to as "numbers". Complex analysis defines the "extended complex numbers", modeled by the [https://en.wikipedia.org/wiki/Riemann_sphere Riemann sphere], which includes a "point at infinity" (and of course you can [https://en.wikipedia.org/wiki/Projectively_extended_real_line extend the real numbers]] similarly). Non-standard analysis defines not only infinite but infinitesimal numbers as [https://en.wikipedia.org/wiki/Hyperreal_number Hyperreal number]s. Granted, I'll agree that using "infitity" without any qualification or context is not really precise enough to do anything useful with. [[Special:Contributions/172.69.23.49\|172.69.23.49]] 03:12, 3 August 2024 (UTC)

	Y'all, the answer is clearly 1. Sincerely, someone who has studied probability.[[Special:Contributions/162.158.137.155\|162.158.137.155]] 14:04, 1 August 2024 (UTC)		Y'all, the answer is clearly 1. Sincerely, someone who has studied probability.[[Special:Contributions/162.158.137.155\|162.158.137.155]] 14:04, 1 August 2024 (UTC)

← Older revision		Revision as of 21:43, 2 August 2024
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	:How about "On, in the context of MK set theory"? MK is a standard way to extend ZFC by allowing classes as mathematical objects, so On (the class of all set-size ordinals) is a class-sized "ordinal". But MK doesn't allow proper classes to be contained in any object, so "On+1" doesn't exist except as a definable hyperclass. Thus, On is the biggest "number" in a model of MK set theory.{{unsigned ip\|172.68.205.151}}		:How about "On, in the context of MK set theory"? MK is a standard way to extend ZFC by allowing classes as mathematical objects, so On (the class of all set-size ordinals) is a class-sized "ordinal". But MK doesn't allow proper classes to be contained in any object, so "On+1" doesn't exist except as a definable hyperclass. Thus, On is the biggest "number" in a model of MK set theory.{{unsigned ip\|172.68.205.151}}
		+
		+	::I personally would not call a class a number, but that is very very subjective! And why would we take a standard extension of ZFC in the first place and not just keep ZFC? yadda yadda yadda you get the idea :) [[Special:Contributions/172.69.246.142\|172.69.246.142]] 21:43, 2 August 2024 (UTC)Bumpf

	Isn’t the joke in the pre-algebra that it would require algebra in order ro calculate? [[Special:Contributions/172.68.70.135\|172.68.70.135]] 20:36, 31 July 2024 (UTC)		Isn’t the joke in the pre-algebra that it would require algebra in order ro calculate? [[Special:Contributions/172.68.70.135\|172.68.70.135]] 20:36, 31 July 2024 (UTC)

@@ Line 87: / Line 87: @@
 Y'all, the answer is clearly 1.  Sincerely, someone who has studied probability.[[Special:Contributions/162.158.137.155|162.158.137.155]] 14:04, 1 August 2024 (UTC)
 No actual cosmologist denotes the Hubble constant in Hz. It's about 70 (km/s)/Mpc. [[Special:Contributions/162.158.41.22|162.158.41.22]] 04:23, 2 August 2024 (UTC)
 :The ''true'' Cosmic cosmologist surely knows that H<sub>0</sub> is 1 (exactly and always), redefining all subsequently derived units in terms of that and the other 'true constants' of the universe... ;) [[Special:Contributions/141.101.99.172|141.101.99.172]] 10:43, 2 August 2024 (UTC)

← Older revision		Revision as of 10:43, 2 August 2024
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	No actual cosmologist denotes the Hubble constant in Hz. It's about 70 (km/s)/Mpc. [[Special:Contributions/162.158.41.22\|162.158.41.22]] 04:23, 2 August 2024 (UTC)		No actual cosmologist denotes the Hubble constant in Hz. It's about 70 (km/s)/Mpc. [[Special:Contributions/162.158.41.22\|162.158.41.22]] 04:23, 2 August 2024 (UTC)
		+	:The ''true'' Cosmic cosmologist surely knows that H<sub>0</sub> is 1 (exactly and always), redefining all subsequently derived units in terms of that and the other 'true constants' of the universe... ;) [[Special:Contributions/141.101.99.172\|141.101.99.172]] 10:43, 2 August 2024 (UTC)