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Miss Pretty :

maybe 3

2026-10-30 13:33:37

1

nadan gudirya :

5[Tears of joy]

2026-10-30 14:09:42

2

Fatima :

3🥰🥰🥰

2026-10-30 05:15:17

3

Muhammad Ali :

3rd wali hun

2026-10-30 12:17:59

4

sana :

4wali

2026-10-30 07:47:02

15

Aqsa :

2

2026-10-30 13:10:54

5

NadeemAhemad :

1 number wali

2026-10-30 11:49:16

5

farha :

black wali

2026-10-30 07:24:49

16

Abdul rouf roufi :

2wali

2026-10-30 10:03:37

5

decent girl :

me2

2026-10-30 07:17:20

10

masoomlarki Pagal 1, :

ma 2🫣

2026-10-30 07:39:05

11

awanmalik458 :

nbr 2

2026-10-30 04:57:35

6

Dreamyzara00 :

3

2026-10-30 06:22:34

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mishal fatima :

no 3 wali

2026-10-30 08:49:32

8

Attitude girl :

koi nhi

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6

💞Mona Arain Brand 💞 :

2

2026-10-30 07:04:07

7

sanam hamdan :

22

2026-10-30 07:59:48

6

Shafique Khan :

1🥰🥰🥰

2026-10-30 08:18:19

9

Zeeshan Haider :

3

2026-10-30 07:06:02

9

cute girl 😍 :

alhamdulillah 2

2026-10-30 08:40:21

12

Cutii♡ :

2

2026-10-30 07:54:39

5

Azlan ❣️😍 :

1 wali

2026-10-30 07:24:53

6

Badnaseeb larki😥 :

2[Heartwarming]

2026-10-30 08:10:12

7

I hat love 💔💔💔💔 :

4 wail huh ma

2026-10-30 09:55:52

8

🫀💖 do dil ak jaan 🫀💖 :

4 wali hun

2026-10-30 08:54:37

21

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$My friend Cho Seung Hee gives 32 hugs Mathematical Games by Martin Gardner Scientific American, November 1977 In an unpublished proof, Graham recently established a bound so vast that it holds the record for the largest number ever used in a serious mathematical proof. The problem that Graham solved belongs to a branch of combinatorics called Ramsey theory, named for the British mathematician Frank Plumpton Ramsey. The field is concerned with properties that are preserved under partitioning. A typical Ramsey problem is to find the minimum number of elements a structure must have to ensure that a certain property holds, regardless of how the structure is divided into parts. Graham’s problem can be stated in terms of an N-dimensional hypercube. Imagine a cube in three dimensions. It has 8 vertices and 12 edges. Now consider a hypercube of N dimensions, which has \(2^{N}\) vertices. Connect every pair of vertices by a straight line. This forms a complete graph with \(2^{N}\) vertices, containing a total of \(2^{N-1}(2^N - 1)\) lines. Now suppose we color every single line in this graph using only two colors: red and blue. We want to know how large N must be before we can guarantee that no matter how the coloring is done, there will always exist four coplanar vertices (vertices that lie on a single flat plane) such that all six lines connecting them are of the same color. Graham, working with Bruce L. Rothschild, proved in 1971 that such a number \(N^{*}\) does exist. However, they could not determine its exact value. They could only establish an upper bound for \(N^{*}\). To express this upper bound, ordinary exponential notation is completely useless. Even the familiar tower of exponents: \(3^{3^{3^{\cdot ^{\cdot ^{\cdot ^{3}}}}}}\) cannot be written down if the tower has more than a few steps, because the number of digits would exceed the number of atoms in the observable universe. To overcome this, Graham used a new arrow notation developed by Donald Knuth. A single arrow \(\uparrow \) signifies ordinary exponentiation. Thus: \(3\uparrow 3=3^{3}=27\) Two arrows \(\uparrow\uparrow\) indicate a tower of exponents: \(3\uparrow \uparrow 3=3\uparrow (3\uparrow 3)=3^{3^{3}}=3^{27}=7,625,597,484,987\) Three arrows \(\uparrow\uparrow\uparrow\) represent a tower of towers, and four arrows \(\uparrow\uparrow\uparrow\uparrow\) represent a tower of towers of towers. Graham began his construction with a number he called g₁: \(g_{1}=3\uparrow \uparrow \uparrow \uparrow 3\) This number g₁ is already so immensely large that it is completely beyond human comprehension. Yet, it is only the first step. Graham then constructed a sequence of 64 numbers, where the number of arrows in each step is determined by the value of the preceding number: \(g_{2}=3\uparrow ^{g_{1}}3\) \(g_{3}=3\uparrow ^{g_{2}}3\) and so on, until he reached: \(g_{64}=3\uparrow ^{g_{63}}3\) This final value, g₆₄, is the upper bound established by Graham. It is a number so unimaginably vast that its digits cannot be written down, nor can they be contained within the boundaries of the known physical universe. It stands as a monument to the staggering scale of combinatorial possibilities. #ez #fyp #xyzbca #rampage #viral #рекомендации$
My friend Cho Seung Hee gives 32 hugs Mathematical Games by Martin Gardner Scientific American, November 1977 In an unpublished proof, Graham recently established a bound so vast that it holds the record for the largest number ever used in a serious mathematical proof. The problem that Graham solved belongs to a branch of combinatorics called Ramsey theory, named for the British mathematician Frank Plumpton Ramsey. The field is concerned with properties that are preserved under partitioning. A typical Ramsey problem is to find the minimum number of elements a structure must have to ensure that a certain property holds, regardless of how the structure is divided into parts. Graham’s problem can be stated in terms of an N-dimensional hypercube. Imagine a cube in three dimensions. It has 8 vertices and 12 edges. Now consider a hypercube of N dimensions, which has \(2^{N}\) vertices. Connect every pair of vertices by a straight line. This forms a complete graph with \(2^{N}\) vertices, containing a total of \(2^{N-1}(2^N - 1)\) lines. Now suppose we color every single line in this graph using only two colors: red and blue. We want to know how large N must be before we can guarantee that no matter how the coloring is done, there will always exist four coplanar vertices (vertices that lie on a single flat plane) such that all six lines connecting them are of the same color. Graham, working with Bruce L. Rothschild, proved in 1971 that such a number \(N^{*}\) does exist. However, they could not determine its exact value. They could only establish an upper bound for \(N^{*}\). To express this upper bound, ordinary exponential notation is completely useless. Even the familiar tower of exponents: \(3^{3^{3^{\cdot ^{\cdot ^{\cdot ^{3}}}}}}\) cannot be written down if the tower has more than a few steps, because the number of digits would exceed the number of atoms in the observable universe. To overcome this, Graham used a new arrow notation developed by Donald Knuth. A single arrow \(\uparrow \) signifies ordinary exponentiation. Thus: \(3\uparrow 3=3^{3}=27\) Two arrows \(\uparrow\uparrow\) indicate a tower of exponents: \(3\uparrow \uparrow 3=3\uparrow (3\uparrow 3)=3^{3^{3}}=3^{27}=7,625,597,484,987\) Three arrows \(\uparrow\uparrow\uparrow\) represent a tower of towers, and four arrows \(\uparrow\uparrow\uparrow\uparrow\) represent a tower of towers of towers. Graham began his construction with a number he called g₁: \(g_{1}=3\uparrow \uparrow \uparrow \uparrow 3\) This number g₁ is already so immensely large that it is completely beyond human comprehension. Yet, it is only the first step. Graham then constructed a sequence of 64 numbers, where the number of arrows in each step is determined by the value of the preceding number: \(g_{2}=3\uparrow ^{g_{1}}3\) \(g_{3}=3\uparrow ^{g_{2}}3\) and so on, until he reached: \(g_{64}=3\uparrow ^{g_{63}}3\) This final value, g₆₄, is the upper bound established by Graham. It is a number so unimaginably vast that its digits cannot be written down, nor can they be contained within the boundaries of the known physical universe. It stands as a monument to the staggering scale of combinatorial possibilities. #ez #fyp #xyzbca #rampage #viral #рекомендации

NOVEMBER RAIN: La canción que convirtió el dolor de amar en una leyenda del rock 🌧️🥀 .. Hay canciones que no se escuchan simplemente… se sienten en lo más profundo del alma. 🎹 November Rain, de Guns N’ Roses, es una obra maestra que nos recuerda que incluso el amor más intenso puede estar marcado por la tristeza, las despedidas y las heridas que deja el tiempo. Una melodía inolvidable que comienza con la sensibilidad de un piano y termina convirtiéndose en una explosión de emociones con uno de los solos de guitarra más legendarios de la historia del rock. 🎸🔥 Porque algunas historias de amor nunca se olvidan… aunque terminen bajo la lluvia. 🌧️🖤 #gunsnroses #novemberrain #lirycs #hardrock #heavymetal @Guns N’ Roses

NOVEMBER RAIN: La canción que convirtió el dolor de amar en una leyenda del rock 🌧️🥀 .. Hay canciones que no se escuchan simplemente… se sienten en lo más profundo del alma. 🎹 November Rain, de Guns N’ Roses, es una obra maestra que nos recuerda que incluso el amor más intenso puede estar marcado por la tristeza, las despedidas y las heridas que deja el tiempo. Una melodía inolvidable que comienza con la sensibilidad de un piano y termina convirtiéndose en una explosión de emociones con uno de los solos de guitarra más legendarios de la historia del rock. 🎸🔥 Porque algunas historias de amor nunca se olvidan… aunque terminen bajo la lluvia. 🌧️🖤 #gunsnroses #novemberrain #lirycs #hardrock #heavymetal @Guns N’ Roses

دستمال یارگاری تو ره ❤️🫠

دستمال یارگاری تو ره ❤️🫠

Flávio Bolsonaro quer tirar Nossa Senhora Aparecida de Padroeira do Brasil? Entenda a verdade sobre a notícia que viralizou e a fake news envolvendo o assunto. 🇧🇷 #FlavioBolsonaro #NossaSenhoraAparecida #lula #FakeNews #Politica

Flávio Bolsonaro quer tirar Nossa Senhora Aparecida de Padroeira do Brasil? Entenda a verdade sobre a notícia que viralizou e a fake news envolvendo o assunto. 🇧🇷 #FlavioBolsonaro #NossaSenhoraAparecida #lula #FakeNews #Politica

Em có tiền mò

Em có tiền mò

Btw this monday I went to Hot Topic to buy a few things I had in mind There was a lot of merch✨ #hotopic#multifandom

Btw this monday I went to Hot Topic to buy a few things I had in mind There was a lot of merch✨ #hotopic#multifandom

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