Tetration - Revision history

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2018-01-12T00:33:17Z

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Admin at 00:33, 12 January 2018

2018-01-12T00:33:02Z

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	Tetration. A bit of background on what tetration is. This notation will let you write what are, unquestionably, the biggest ~~number~~ you've ever seen in your life.		Tetration. A bit of background on what tetration is. This notation will let you write what are, unquestionably, the biggest numbers you've ever seen in your life.

	Notation for progressively larger numbers.		Notation for progressively larger numbers.
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	See also: the Knuth up arrow http://mathworld.wolfram.com/PowerTower.html		See also: the Knuth up arrow http://mathworld.wolfram.com/PowerTower.html


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Admin at 08:48, 8 January 2018

2018-01-08T08:48:08Z

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	See also: the Knuth up arrow http://mathworld.wolfram.com/PowerTower.html		See also: the Knuth up arrow http://mathworld.wolfram.com/PowerTower.html

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Admin: Created page with "Tetration. A bit of background on what tetration is. This notation will let you write what are, unquestionably, the biggest number you've ever seen in your life. Notation for..."

2017-07-16T05:48:17Z

Created page with "Tetration. A bit of background on what tetration is. This notation will let you write what are, unquestionably, the biggest number you've ever seen in your life. Notation for..."

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Tetration. A bit of background on what tetration is. This notation will let you write what are, unquestionably, the biggest number you've ever seen in your life.

Notation for progressively larger numbers.

5 tetrated can be written as 5 to the power of 5^5^5^5 mod 10, mod 11

Consider the number 4. To make a larger number out of 4, you might add 4 to 4 and get 8. You might multiply by 4 to get 16. Or you might raise 4 to the power of itself: 4^4, or 256. But what if you took that a step further: Raise 4 to the power of 4, 4 times:

<math>
4^{4^{4^{4}}}
</math>

That's 4 tetrated, or <math>{^{4} 4}</math>. That's a very, very, very big number:

<math>4^{4^{4^{4}}} = 4^{4^{256}} = 4^{ 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096 }</math>

And that's just FOUR tetrated.

Imagine 10 tetrated. 20, 30, 40 tetrated. 100 tetrated. A googol tetrated.

Time for a puzzle.

What is the remainder when you divide

<math>
4^{ 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096 }
</math>

by 11?

See also: the Knuth up arrow http://mathworld.wolfram.com/PowerTower.html