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In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. [ 1 ] In his 1947 paper, [ 2 ] R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations .
For example, quotient set, quotient group, quotient category, etc. 3. In number theory and field theory, / denotes a field extension, where F is an extension field of the field E. 4. In probability theory, denotes a conditional probability. For example, (/) denotes the probability of A, given that B occurs.
The calculations for finding the fourth digit from the example above are illustrated at right. The arrow from the nine will always point to the digit of the multiplicand directly above the digit of the answer you wish to find, with the other arrows each pointing one digit to the right. Each arrow head points to a UT Pair, or Product Pair.
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though Knuth's up arrow notation and the left-exponent are common.
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The use of the caret for exponentiation can be traced back to ALGOL 60, [citation needed] which expressed the exponentiation operator as an upward-pointing arrow, intended to evoke the superscript notation common in mathematics. The upward-pointing arrow is now used to signify hyperoperations in Knuth's up-arrow notation.
Unlike a number line, which extends horizontally and infinitely, the Math Arrow displays the whole numbers from 0 to 100 in a pair of parallel zigzag lines. [2] The numbers on the left-hand zigzag run from 0 at the bottom to 50 at the top; on the right-hand zigzag they run from 50 at the top to 100 at the bottom (the number 50 appears twice, at the top of both zigzags).