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'''Googlek''' is equal to \(16^{256} = 2^{1024}\), intended as a hexadecimal analog of [[googol]].<ref>{{cite web|authorlink=Intuitor|url=http://www.intuitor.com/hex/words.html|title=Hexadecimal Number Words|accessdate=November 2015}}</ref> It was described on a page on the site "intuitor.com" which proposes a method for pronouncing numbers in hexadecimal. To the best of our knowledge, the page was written in 2007 by Tom Rogers, a high school teacher in South Carolina, USA. |
'''Googlek''' is equal to \(16^{256} = 2^{1024}\), intended as a hexadecimal analog of [[googol]].<ref>{{cite web|authorlink=Intuitor|url=http://www.intuitor.com/hex/words.html|title=Hexadecimal Number Words|accessdate=November 2015}}</ref> It was described on a page on the site "intuitor.com" which proposes a method for pronouncing numbers in hexadecimal. To the best of our knowledge, the page was written in 2007 by Tom Rogers, a high school teacher in South Carolina, USA. |
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+ | It is approximately \(1.797 \times 10^{308}\), or 179.769 [[uncentillion]] in the short scale and about 179.769 [[unquinquagintillion]] in the long scale. |
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⚫ | |||
⚫ | It is the smallest power of two not expressible as a double-precision floating point number according to IEEE 754 (a double has an exponent width of 11 bits, one of which is the sign, so the exponent has a maximum of 2<sup>10</sup> - 1). As a result, it is the floating-point limit for numbers in many programming languages. For example, numbers equal to this or larger in JavaScript will simply be expressed as "Infinity". |
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⚫ | |||
+ | JavaScript [[HyperCalc]] maxes out at a [[power tower]] of tens this many terms high, or \(10\uparrow\uparrow(2^{1024})\). |
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+ | 2^1024 is the maximum amount of money, coins etc. for games like ''[[AdVenture Capitalist]]'' or ''[[Cookie Clicker]]''. |
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⚫ | |||
+ | |||
+ | Username5243 calls this number '''Binary-Goodcolplex'''.<ref>[https://sites.google.com/site/mylargenumbers/numbers/unan/p1 Part 1 - My Large Numbers]</ref> |
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+ | |||
+ | == Digit expansions == |
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+ | Its full decimal expansion is: |
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+ | |||
⚫ | {{digits|179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216}} |
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+ | |||
+ | Its full hexadecimal expansion is: |
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+ | |||
+ | {{digits|10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}} |
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+ | |||
+ | Its full binary expansion is: |
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+ | |||
+ | {{digits|10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}} |
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+ | |||
+ | ==Approximations== |
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+ | {| border="0" cellpadding="1" cellspacing="1" class="article-table" |
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+ | |- |
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+ | ! scope="col"|Notation |
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+ | ! scope="col"|Lower bound |
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+ | ! scope="col"|Upper bound |
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+ | |- |
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+ | |[[Scientific notation]] |
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+ | |\(1.797\times10^{308}\) |
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+ | |\(1.798\times10^{308}\) |
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+ | |- |
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+ | |[[Arrow notation]] |
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+ | |colspan="2" align="center"|\(16\uparrow256\) |
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+ | |- |
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+ | |[[Steinhaus-Moser Notation]] |
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+ | |143[3] |
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+ | |144[3] |
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+ | |- |
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+ | |[[Copy notation]] |
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+ | |1[309] |
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+ | |2[309] |
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+ | |- |
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+ | |[[Taro's multivariable Ackermann function]] |
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+ | |A(3,1021) |
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+ | |A(3,1022) |
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+ | |- |
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+ | |[[Pound-Star Notation]] |
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+ | |#*((560))*11 |
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+ | |#*((561))*11 |
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+ | |- |
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+ | |[[BEAF]] |
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+ | |colspan="2" align="center"|{16,256} |
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+ | |- |
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+ | |[[Hyper-E notation]] |
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+ | |colspan="2" align="center"|E[16]2#2 |
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+ | |- |
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+ | |[[Bashicu matrix system]] |
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+ | |colspan="2" align="center"|(0)(0)(0)(0)(0)(0)[65536] |
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+ | |- |
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+ | |[[Hyperfactorial array notation]] |
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+ | |170! |
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+ | |171! |
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+ | |- |
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+ | |[[Fast-growing hierarchy]] |
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+ | |\(f_2(1014)\) |
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+ | |\(f_2(1015)\) |
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+ | |- |
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+ | |[[Hardy hierarchy]] |
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+ | |\(H_{\omega^2}(1014)\) |
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+ | |\(H_{\omega^2}(1015)\) |
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+ | |- |
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+ | |[[Slow-growing hierarchy]] |
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+ | |colspan="2" align="center"|\(g_{\omega^{\omega^2}}(16)\) |
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+ | |} |
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+ | |||
⚫ | |||
<references /> |
<references /> |
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+ | {{Numbers by Username5243}} |
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[[Category:Numbers]] |
[[Category:Numbers]] |
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[[Category:Class 2]] |
[[Category:Class 2]] |
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[[Category:Powers of 2]] |
[[Category:Powers of 2]] |
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+ | [[Category:Googol series]] |
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+ | [[Category:Numbers with 101 to 999 digits]] |
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+ | [[Category:Computers]] |
Revision as of 09:29, 5 July 2018
Googlek is equal to \(16^{256} = 2^{1024}\), intended as a hexadecimal analog of googol.[1] It was described on a page on the site "intuitor.com" which proposes a method for pronouncing numbers in hexadecimal. To the best of our knowledge, the page was written in 2007 by Tom Rogers, a high school teacher in South Carolina, USA.
It is approximately \(1.797 \times 10^{308}\), or 179.769 uncentillion in the short scale and about 179.769 unquinquagintillion in the long scale.
It is the smallest power of two not expressible as a double-precision floating point number according to IEEE 754 (a double has an exponent width of 11 bits, one of which is the sign, so the exponent has a maximum of 210 - 1). As a result, it is the floating-point limit for numbers in many programming languages. For example, numbers equal to this or larger in JavaScript will simply be expressed as "Infinity".
JavaScript HyperCalc maxes out at a power tower of tens this many terms high, or \(10\uparrow\uparrow(2^{1024})\).
2^1024 is the maximum amount of money, coins etc. for games like AdVenture Capitalist or Cookie Clicker.
Username5243 calls this number Binary-Goodcolplex.[2]
Digit expansions
Its full decimal expansion is:
Its full hexadecimal expansion is:
Its full binary expansion is:
Approximations
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1.797\times10^{308}\) | \(1.798\times10^{308}\) |
Arrow notation | \(16\uparrow256\) | |
Steinhaus-Moser Notation | 143[3] | 144[3] |
Copy notation | 1[309] | 2[309] |
Taro's multivariable Ackermann function | A(3,1021) | A(3,1022) |
Pound-Star Notation | #*((560))*11 | #*((561))*11 |
BEAF | {16,256} | |
Hyper-E notation | E[16]2#2 | |
Bashicu matrix system | (0)(0)(0)(0)(0)(0)[65536] | |
Hyperfactorial array notation | 170! | 171! |
Fast-growing hierarchy | \(f_2(1014)\) | \(f_2(1015)\) |
Hardy hierarchy | \(H_{\omega^2}(1014)\) | \(H_{\omega^2}(1015)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^2}}(16)\) |
Sources
- ↑ Hexadecimal Number Words. Retrieved November 2015.
- ↑ Part 1 - My Large Numbers
Megoogol · Meg-Googol · Meg-Doogol · Meg-Kiloogol · Meg-Kil-Googol · Meg-Dukiloogol · Meg-Trukiloogol · Dumegoogol · Dumeg-Googol · Dumeg-Kiloogol · Dumeg-Dukiloogol · Trumegoogol · Trumeg-Kiloogol · Tetrumegoogol · Pentumegoogol · Gigoogol · Gig-Googol · Gig-Kiloogol · Gig-Megoogol · Dugigoogol · Trugigoogol · Teroogol · Duteroogol · Truteroogol · Petoogol · Ectoogol · Zettoogol · Yottoogol · Xennoogol · Wekoogol
Note: The readers should be careful that numbers defined by Username5243's Array Notation are ill-defined as explained in Username5243's Array Notation#Issues. So, when an article refers to a number defined by the notation, it actually refers to an intended value, not an actual value itself (for example, a[c]b = \(a \uparrow^c b\) in arrow notation). In addition, even if the notation is ill-defined, a class category should be based on an intended value when listed, not an actual value itself, as it is not hard to fix all the issues from the original definition, hence it should not be removed.