Graham's Number
look it up, it is the largest by proof so far.
2006-12-17 02:28:12
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answer #1
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answered by ioniceclipse 2
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Numbers arranged in ascending order:
1. Avogadro's number, 6.0221415x10^23, can loosely be thought of as the number of hydrogen atoms in a gram of hydrogen gas, and is perhaps the most widely known large number from chemistry and physics. Avogadro's number is much less than a googol.
2. A little googol is 2^100, or about 1.267x1030
3.10^100= googol
A googol is greater than the number of particles in the known universe, which has been variously estimated from 10^72 up to 10^87.
4. The Shannon number is a rough estimate of the number of possible chess games, and it is very much more than a googol, around the order of 10^120.
5. A googol is considerably less than the number described in the ancient Greek story of The Sand Reckoner, namely 10^(8*10^16)
6. A little googolplex is 2^(2^100)
7.In number theory, Skewes' number can refer to several extremely large numbers used by the South African mathematician Stanley Skewes.
By definition, the number is the smallest natural number x for which
Ï(x) â Li(x) ⥠0
8. Graham's number, named after Ronald Graham, is often described as the largest number that has ever been seriously used in a mathematical proof. It is too large to be written in scientific notation because even the digits in the exponent would exceed the number of particles in the visible universe, so it needs special notation to write down. Graham's number is much, much larger than other well known large numbers such as a googol and a googolplex.
9. Infinity- although its not a number.
2006-12-17 10:22:32
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answer #2
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answered by Som™ 6
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Infinity is not really a number, more of an idea or a theory. A google is a one(1) followed by one hundred zeros and a googleplex is one google raised to the googleth power. But there is always a number higher. To get the idea of a googleplex, there has never been a googleplex leaves in the entire history of the world. That includes blades of grass, pine needles, etc. All the leaves added up for all of the millions of years would not add up to a googleplex. Pretty big number.
2006-12-17 10:31:54
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answer #3
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answered by Anonymous
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0 is the biggest number in the world.
2006-12-17 10:40:30
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answer #4
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answered by chenho 3
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There's no biggest number in the world, it's infinity.
2006-12-17 10:23:42
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answer #5
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answered by Lai Yu Zeng 4
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The googolplex is the highest placeholder in the world. It also can be called milli-millillion. Infinity is a "number" that cannot be thought of.
2006-12-17 10:26:49
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answer #6
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answered by Lightbringer 6
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googol is the large number 10100, that is, the digit 1 followed by one hundred zeros (in decimal representation). One way of grasping its size is to multiply 1,000,000 by itself 16 times, then multiply the result by ten thousand. The ultimate product of this operation is one googol (10100). The term was coined in 1920 by nine-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. Kasner popularized the concept in his book Mathematics and the Imagination.
A googol is of the same order of magnitude as the factorial of 70 (70! being approximately 1.198 googol, or 10 to the power 100.0784), and its only prime factors are 2 and 5 (100 of each). In binary it would take up 333 bits.
The googol is of no particular significance in mathematics, but is useful when comparing with other incredibly large quantities such as the number of subatomic particles in the visible universe or the number of possible chess games. Kasner created it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics.
The Internet search engine Google was named after this number. Larry Page, one of the founders, was fascinated with mathematics and 'Googol', even during high school. They ended up with 'Google' due to a spelling mistake on a cheque that investors wrote to the founders.
Googolplex is the number .
It can also be written as 10googol, or
,
or as a 1 followed by a googol (10100) zeroes. In 1938, Edward Kasner and his nephews Edwin and Milton Sirotta coined the term "googol." Milton then proposed the term "googolplex" to be "one, followed by writing zeroes until you got tired." Kasner decided to adopt a more formal definition "because different people get tired at different times and it would never do to have Carnera [a champion boxer] a better mathematician than Dr. Einstein, simply because he had more endurance."[1]
How big is a googolplex?
One googol is greater than the number of elementary particles in the known universe, which has been variously estimated from 1072 up to 1087. Since a googolplex is one followed by a googol zeroes, it would not be possible to write down or store a googolplex in decimal notation, even if all the matter in the known universe were converted into paper and ink or disk drives.
Thinking of this another way, consider printing the digits of a googolplex in unreadable, 1-point font. TeX 1pt font is .3514598mm per digit, which means it would take about meters to write in one point font. The known universe is estimated at meters in diameter, which means the distance to write the digits would be about times the diameter of the known universe. The time it would take to write such a number also renders the task implausible: if a person can write two digits per second, it would take around times the age of the universe to write down a googolplex.
Thus in the physical world it is difficult to give examples of numbers that compare closely to a googolplex. In analyzing quantum states and black holes, Physicist Don Page writes that "determining experimentally whether or not information is lost down black holes of solar mass ... would require more than measurements to give a rough determination of the final density matrix after black hole evaporates."[1] In a separate article, Page shows that the number of states in a black hole with a mass roughly equivalent to the Andromeda Galaxy is in the range of a googolplex.[2]
In pure mathematics, the magnitude of a googolplex is not as large as some of the specially defined extraordinarily large numbers, such as those written with tetration, Knuth's up-arrow notation, Steinhaus-Moser notation, or Conway chained arrow notation. Even more simply, one can name numbers larger than a googolplex with fewer symbols, for example,
,
is much larger. This last number can be expressed more concisely as using tetration, or using up-arrow notation.
Some sequences grow very quickly; for instance, the first two Ackermann numbers are 1 and 4, but then the third is , a power tower of threes more than seven trillion high. Yet, much larger still is Graham's number, perhaps the largest natural number mathematicians actually have a use for.
A googolplex is a huge number that can be expressed compactly because of nested exponentiation. Other procedures (like tetration) can express large numbers even more compactly. The natural question is: what procedure uses the smallest number of symbols to express the biggest number? A Turing machine formalizes the notion of a procedure, and a busy beaver is the Turing machine of size n that can write down the biggest possible number [3]. The bigger n is, the more complex the busy beaver, hence the bigger the number it can write down. For n=1, 2, 3, 4 and 5 the numbers expressible are not huge, but research as of 2006 shows that for n=6 the busy beaver can write down a number at least as big as .[4] It is an open question whether the seventh busy beaver can express a googolplex.
2006-12-19 23:29:03
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answer #7
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answered by ash 3
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If there were a biggest number, you could add one and get a bigger number. Contradiction, there is no biggest number.
2006-12-17 10:58:08
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answer #8
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answered by Professor Maddie 4
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One rolled with the paper on the cheech and chong album
2006-12-17 10:22:22
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answer #9
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answered by cry baby gator 4
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the numbers go on and on forever
2006-12-17 10:26:31
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answer #10
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answered by Imperfection At Its Finest. 4
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