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@tiemnhabemay: thoa sữa dưỡng ẩm mỗi ngày, da bé được bảo vệ và mềm mịn hơn #xuhuong #mevabe #mebimsua #kemduongamchobe

Tiệm Nhà Bé Mây
Tiệm Nhà Bé Mây
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Wednesday 03 December 2025 05:48:58 GMT
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Re-upload me and bro Graham’s number is one of the largest numbers ever used in a serious mathematical proof. It appeared in work by mathematicians Ronald Graham and Bruce Lee Rothschild on a problem in combinatorics (a branch of math about patterns and connections). The number is so huge that: * you cannot write all its digits, * there is not enough space in the observable universe to store them, * even the number of digits is unimaginably gigantic. But it is still finite. Step 1: Understand arrows Graham’s number uses Knuth’s up-arrow notation. Normal operations grow like this: 3+3=6,\quad 3\times3=9,\quad 3^3=27 Then arrows continue the pattern: 3\uparrow\uparrow 3 = 3^{3^3} = 3^{27} That equals: 7,625,597,484,987 Already large, but tiny compared with what comes next. Step 2: Triple arrows Now: 3\uparrow\uparrow\uparrow 3 = 3\uparrow\uparrow(3\uparrow\uparrow3) This means a power tower of 3s whose height is itself enormous. You cannot realistically write the value down. Step 3: Four arrows The first stage of Graham’s construction is: g_1 = 3\uparrow\uparrow\uparrow\uparrow 3 This is already vastly beyond numbers like: * a googol = 10^{100} * a googolplex = 10^{10^{100}} Step 4: Building Graham’s number Now define: g_{n+1}=3\uparrow^{g_n}3 Meaning: * take the previous number g_n, * use it as the number of arrows between the 3s. So: * g_2 has g_1 arrows, * g_3 has g_2 arrows, * and so on. Graham’s number is g_{64}. Simple analogy Imagine: * exponentiation is a firecracker, * double arrows are a bomb, * triple arrows are a planet explosion, * Graham’s number is like stacking universes of explosions recursively 64 times. Weird fact Even though Graham’s number is unimaginably huge, mathematicians know its last digit: G\equiv 7\pmod{10} So Graham’s number ends in 7. Important idea There are numbers much larger than Graham’s number, such as: * TREE(3) * Busy Beaver numbers But Graham’s number became famous because it was one of the first “mind-breakingly huge” numbers used in mainstream mathematics.#tcd #paris2015 #crocuscityhall2024 #twd #dcb
Re-upload me and bro Graham’s number is one of the largest numbers ever used in a serious mathematical proof. It appeared in work by mathematicians Ronald Graham and Bruce Lee Rothschild on a problem in combinatorics (a branch of math about patterns and connections). The number is so huge that: * you cannot write all its digits, * there is not enough space in the observable universe to store them, * even the number of digits is unimaginably gigantic. But it is still finite. Step 1: Understand arrows Graham’s number uses Knuth’s up-arrow notation. Normal operations grow like this: 3+3=6,\quad 3\times3=9,\quad 3^3=27 Then arrows continue the pattern: 3\uparrow\uparrow 3 = 3^{3^3} = 3^{27} That equals: 7,625,597,484,987 Already large, but tiny compared with what comes next. Step 2: Triple arrows Now: 3\uparrow\uparrow\uparrow 3 = 3\uparrow\uparrow(3\uparrow\uparrow3) This means a power tower of 3s whose height is itself enormous. You cannot realistically write the value down. Step 3: Four arrows The first stage of Graham’s construction is: g_1 = 3\uparrow\uparrow\uparrow\uparrow 3 This is already vastly beyond numbers like: * a googol = 10^{100} * a googolplex = 10^{10^{100}} Step 4: Building Graham’s number Now define: g_{n+1}=3\uparrow^{g_n}3 Meaning: * take the previous number g_n, * use it as the number of arrows between the 3s. So: * g_2 has g_1 arrows, * g_3 has g_2 arrows, * and so on. Graham’s number is g_{64}. Simple analogy Imagine: * exponentiation is a firecracker, * double arrows are a bomb, * triple arrows are a planet explosion, * Graham’s number is like stacking universes of explosions recursively 64 times. Weird fact Even though Graham’s number is unimaginably huge, mathematicians know its last digit: G\equiv 7\pmod{10} So Graham’s number ends in 7. Important idea There are numbers much larger than Graham’s number, such as: * TREE(3) * Busy Beaver numbers But Graham’s number became famous because it was one of the first “mind-breakingly huge” numbers used in mainstream mathematics.#tcd #paris2015 #crocuscityhall2024 #twd #dcb
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