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<img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon"><img src="https://community.akamai.steamstatic.com/economy/emoticon/missing" alt=":missing:" class="emoticon">greek god

Other writers refer to a similar question without the three dots. I wish I knew how to determine if questions have been edited. But that’s me whining.

Numbers such as this are very cleverly constructed to violate one’s perception that they are rational. Recall that the definition of a rational number is that it can be written as pq where p and q are integers and q is not 0 .

Try to imagine, if anyone can do so anymore, the long division process of dividing p by q . This division is happening to investigation what rationals look like when converted to decimals.

One of two things will happen during the long division. There might be no remainder (the long division remainder which happens after every subtraction) in which case the decimal terminates. Or the remainder might never be 0. When dividing by q, there are at most q−1 remainders (the long division variety) and hence the decimal will repeat after at most q−1 division steps.

We conclude that the decimal form of a rational number either terminates or is an infinite repeating decimal.

Your number looks like it repeats. True, its pattern repeats but the decimal does not and so is irrational.

<img src="https://community.akamai.steamstatic.com/economy/emoticon/ok_ay" alt=":ok_ay:" class="emoticon">Proof that zero is less than one<img src="https://community.akamai.steamstatic.com/economy/emoticon/ok_ay" alt=":ok_ay:" class="emoticon">
In this note we will prove that 0 < 1. In order to do so we first need a lemma.
Lemma. For any real number x we have x
2 ≥ 0.
Proof. We will consider two cases: x ≥ 0 and x < 0. In the first case x ≥ 0 we have
x
2 = x · x
≥ 0 · 0 by (O5)
= 0 by §1.1 #4.
In the second case x < 0 we have −x ≥ 0 by Proposition 1.1.1(d), and hence
x
2 = x · x
= (−x)(−x) by Proposition 1.1.1(c)
≥ 0 · 0 by (O5) since − x ≥ 0
= 0 by §1.1 #4.
Hence for any real number x we have x
2 ≥ 0.
Claim. We have 0 < 1.
Proof. First we will show 0 ≤ 1. To see this, note that
1 = 1 · 1 by (P7)
≥ 0 by our Lemma above.
Now it suffices to show that 0 6= 1. Indeed, suppose for a contradiction that 0 = 1. Choose
any real number x 6= 0 that is nonzero1
. Note that we have
x = x · 1 by (P7)
= x · 0 since we’ve assumed for a contradiction that 0 = 1
= 0 by §1.1 Problem #4.
This contradicts the fact that we chose x 6= 0, and hence it must be the case that 0 6= 1.
We have shown 0 ≤ 1 and 0 6= 1, and together these imply 0 < 1.

Pythagorean Theorem
Quite possible the most famous theorem in mathematics, Pythagoras’ Theorem states that square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Whether Pythagoras (c.560-c.480 B.C.) or someone else from his School was the first to discover its proof can’t be claimed with any degree of credibility. Euclid’s (c 300 B.C.) Elements is considered the first proof of the theorem, but far from being the only one. There are at least 114 approaches to proving the theorem. Mathematician Bhaskara (about 1114-1185) proved the Pythagorean Theorem simply by drawing this picture and saying “Behold!”

Достижения

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Игра		#	Открытые достижения				Закрытые достижения
			Лучшие из текущих	#	Очки	%	Следующие самые легкие	#	Очки	%
	10 Second Ninja X	12	-1	0	0,00	0	1.2863891125	12	17,88	100
	The Adventures of Capitano Navarro	6	-1	0	0,00	0	1.5594174862	6	10,81	100
	The Adventures of Tree	103	-1	0	0,00	0	1.4894055128	103	206,01	100
	Aegis Defenders	31	-1	0	0,00	0	0.9853649139	31	55,95	100
	Apex Legends	12	0.3733288348	3	0,99	25	0.3870141208	9	4,76	75
	Block N Load	66	-1	0	0,00	0	0.3327751160	66	97,36	100
	Brawlhalla	65	1.2153223753	28	25,74	43,1	1.0527930260	37	69,13	56,9
	Business Tour - Online Multiplayer Board Game	19	-1	0	0,00	0	0.4744524658	19	27,36	100
	Castle Crashers	12	0.5271779895	2	0,83	16,7	0.5955290794	10	10,62	83,3
	ClearMem :: Free Up Your RAM	13	0.6630893350	13	4,86	100	100	0	0,00	0
	Counter-Strike 2	1	0.6957119703	1	0,70	100	100	0	0,00	0
	Dear Esther: Landmark Edition	10	-1	0	0,00	0	1.1834261417	10	13,46	100
	Deponia: The Complete Journey	105	-1	0	0,00	0	0.7800586820	105	145,73	100
	Destiny 2	13	-1	0	0,00	0	0.2175190300	13	8,32	100
	DiRT 3 Complete Edition	60	0.5389568210	2	0,99	3,3	0.7818034291	58	84,55	96,7
	DiRT Rally	170	-1	0	0,00	0	0.4817809165	170	293,97	100
	Drawful 2	10	1.0923883915	5	4,96	50	1.3418166637	5	9,39	50
	The Dwarves	34	-1	0	0,00	0	1.0369824171	34	58,10	100
	Euro Truck Simulator 2	39	0.9020575285	12	5,97	30,8	0.5652992725	27	45,42	69,2
	F1 2015	45	-1	0	0,00	0	1.3252829313	45	85,71	100
	F1 2018	50	0.9889645576	1	0,99	2	0.8901318908	49	76,36	98
	Fall Guys	34	0.0715423450	6	0,26	17,6	0.0743351728	28	15,76	82,4
	Find You	7	-1	0	0,00	0	0.7808784246	7	10,82	100
	Fishing Planet	17	-1	0	0,00	0	0.7561569810	17	31,71	100
	The Flame in the Flood	36	-1	0	0,00	0	1.0728082657	36	67,83	100
	Fluffy Creatures VS The World	3	-1	0	0,00	0	1.1827241182	3	3,75	100
	Friday the 13th: Killer Puzzle	44	0.7563720345	16	8,71	36,4	0.5284975767	28	31,06	63,6
	Friday the 13th: Killer Puzzle - Episode 2: Lockdown	1	0.0028659597	1	0,00	100	100	0	0,00	0
	Garry's Mod	29	0.7695979476	8	2,73	27,6	0.5564160347	21	23,80	72,4
	GOAT OF DUTY	31	-1	0	0,00	0	1.5253871679	31	62,93	100
	Grand Theft Auto V Legacy	77	0.7477425337	22	7,96	28,6	0.1846452504	55	45,32	71,4
	GRID 2	50	0.6494847536	4	2,07	8	0.6738467216	46	55,01	92
	The Haunting of Billy	9	-1	0	0,00	0	1.7648202181	9	17,80	100
	Hide and Shriek	20	0.7885501385	1	0,79	5	0.5623266101	19	28,72	95
	Injustice: Gods Among Us Ultimate Edition	50	-1	0	0,00	0	0.6358305216	50	73,28	100
	Interkosmos	17	-1	0	0,00	100	2.2490203381	17-17	38,54	100
	JASEM: Just Another Shooter with Electronic Music	19	1.0728044510	1	1,07	5,3	1.2712788582	18	33,70	94,7
	Just Cause 2	50	0.3109485507	4	1,03	8	0.5441230536	46	48,78	92
	Kao the Kangaroo: Round 2	9	-1	0	0,00	0	1.2721562386	9	14,06	100
	KurtzPel	85	-1	0	0,00	16,5	0.2788993120	85-14	104,58	100
	Lara Croft and the Temple of Osiris	40	-1	0	0,00	0	1.0696423054	40	63,60	100
	Layers of Fear (2016)	18	1.2029249668	8	6,42	44,4	1.0045119524	10	15,22	55,6
	Left 4 Dead 2	101	0.8904144168	7	3,11	6,9	0.2312088460	94	99,26	93,1
	The LEGO® NINJAGO® Movie Video Game	50	0.9758626223	3	2,88	6	1.1148422956	47	70,35	94
	LEGO® The Hobbit™	39	-1	0	0,00	0	0.7857066393	39	50,01	100
	Life is Strange™	12	0.3499483764	1	0,35	8,3	0.4499438703	11	7,95	91,7
	The MagiCats Best Of	83	-1	0	0,00	0	2.4572329521	83	203,95	100
	Minion Masters	38	-1	0	0,00	0	0.8990642428	38	49,70	100
	Muck	49	0.1527281553	1	0,15	2	0.3568329215	48	58,96	98
	Niche - a genetics survival game	31	-1	0	0,00	0	0.7033563852	31	66,44	100
	No More Room in Hell	115	0.7570917606	3	1,73	2,6	0.8507970572	112	204,25	97,4
	PAC-MAN™ CHAMPIONSHIP EDITION 2	18	1.1562640667	3	3,17	16,7	1.2714655399	15	25,92	83,3
	Paladins	58	1.6881543398	58	42,51	100	100	0	0,00	0
	PAYDAY 2	715	0.9879305959	32	17,50	4,5	0.3211263418	683	835,33	95,5
	PAYDAY 2: Gage Weapon Pack #02	10	0.0070038945	1	0,01	10	0.5236302018	9	6,08	90
	PAYDAY 2: The Butcher's AK/CAR Mod Pack	8	0.0140861142	1	0,01	12,5	0.4996674955	7	5,01	87,5
	PickCrafter	121	1.2502472401	96	51,93	79,3	1.0223273039	25	46,88	20,7
	Pixel Battle Royale	11	0.4713257253	1	0,47	9,1	0.7510658503	10	10,24	90,9
	Portal 2	51	0.3744655252	4	1,02	7,8	0.1811803728	47	30,56	92,2
	Pressure	22	-1	0	0,00	0	1.0105385780	22	33,40	100
	Professional Farmer 2017	30	-1	0	0,00	0	1.1568704844	30	56,15	100
	Q.U.B.E. 2	15	-1	0	0,00	0	0.8552578688	15	16,33	100
	Realm Royale Reforged	22	1.1393300295	8	6,82	36,4	0.8691021800	14	18,47	63,6
	Red Wings	29	-1	0	0,00	0	1.3798192739	29	61,64	100
	Risen	50	-1	0	0,00	0	1.4299340248	50	94,31	100
	Robocraft	43	1.9317396879	16	23,99	37,2	1.5467236042	27	49,26	62,8
	SCP: Escape Together	10	-1	0	0,00	0	1.3517663479	10	17,34	100
	SCP: Secret Laboratory	52	0.7157276273	9	4,32	17,3	0.4769651592	43	77,35	82,7
	SEGA Mega Drive & Genesis Classics	25	1.4461377859	1	1,45	4	1.5567010641	24	51,36	96
	Shooty Skies	29	-1	0	0,00	0	0.7516672611	29	34,61	100
	Showdown Bandit	8	-1	0	0,00	0	1.9161219597	8	16,33	100
	Sid Meier's Ace Patrol	52	-1	0	0,00	0	0.9503597021	52	95,56	100
	Skillshot City	40	-1	0	0,00	0	1.2219266891	40	78,92	100
	Sleeping Dogs: Definitive Edition	59	0.9694486856	28	18,64	47,5	0.8306597471	31	34,65	52,5
	Snail Racer Extreme	10	-1	0	0,00	0	1.1036366224	10	11,61	100
	Snake Pass	33	-1	0	0,00	0	0.7761667967	33	53,43	100
	Spec Ops: The Line	50	0.8366555572	28	16,28	56	0.4882775545	22	19,75	44
	Steel Rats	46	-1	0	0,00	0	1.4044857025	46	95,83	100
	A Story About My Uncle	15	1.0680073500	1	1,07	6,7	1.5488197803	14	23,31	93,3
	Sundered: Eldritch Edition	20	-1	0	0,00	0	0.6791258454	20	24,88	100
	Team Fortress 2	520	1.1442942619	131	64,50	25,6	0.2652967870	389-2	292,20	74,4
	Tell Me Why	30	-1	0	0,00	0	1.1061640978	30	43,84	100
	Terraria	137	0.3666049838	16	3,99	11,7	0.2167529017	121	128,47	88,3
	Titan Quest Anniversary Edition	76	-1	0	0,00	0	0.6314987540	76	130,25	100
	Tomb Raider	50	0.7649637461	15	7,44	30	0.4690930247	35	38,69	70
	Total War: SHOGUN 2	106	-1	0	0,00	0	0.5141721368	106	166,49	100
	Trailer Park Boys: Greasy Money	21	0.4729592800	2	0,88	9,5	0.6283998489	19	15,29	90,5
	Trove	19	1.4002990723	2	2,30	10,5	1.1099474430	17	27,27	89,5
	Trucks & Trailers	35	-1	0	0,00	0	1.0176596642	35	60,02	100
	Tumblestone	28	-1	0	0,00	0	1.3105792999	28	49,95	100
	The Uncertain: Last Quiet Day	32	-1	0	0,00	0	1.1425333023	32	43,82	100
	Unturned	95	1.2724413872	30	20,02	31,6	0.7718029618	65	154,64	68,4
	Warhammer Underworlds - Shadespire Edition	38	-1	0	0,00	0	1.9590020180	38	84,00	100
	We Were Here	26	0.3981259465	8	2,89	30,8	0.3139082491	18	9,15	69,2
	Will Glow the Wisp	20	-1	0	0,00	0	1.2528418303	20	31,53	100
	Will To Live Online	44	-1	0	0,00	0	0.9001083374	44	62,90	100
	Wrecked	13	-1	0	0,00	0	0.7228548527	13	20,79	100
	Zula Europe	59	1.3458583355	14	11,25	23,7	0.9650353789	45	68,88	76,3

Бета-игры

Игра		#	Открытые достижения				Закрытые достижения
			Лучшие из текущих	#	Очки	%	Следующие самые легкие	#	Очки	%
	Gothic Playable Teaser	25	-1	0	0,00	0	1.1403752565	25	40,54	100

Профиль последний раз обновлен: 26 сентября 2024 г. в 11:41 .

Следующее автоматическое обновление: 28 октября 2026 г. в 10:39 .