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  2. Inclusion–exclusion principle - Wikipedia

    en.wikipedia.org/wiki/Inclusion–exclusion...

    Euler's totient or phi function, φ(n) is an arithmetic function that counts the number of positive integers less than or equal to n that are relatively prime to n. That is, if n is a positive integer , then φ( n ) is the number of integers k in the range 1 ≤ k ≤ n which have no common factor with n other than 1.

  3. Floor and ceiling functions - Wikipedia

    en.wikipedia.org/wiki/Floor_and_ceiling_functions

    In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]

  4. Numeric precision in Microsoft Excel - Wikipedia

    en.wikipedia.org/wiki/Numeric_precision_in...

    Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...

  5. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    Floor function: Largest integer less than or equal to a given number. Ceiling function: Smallest integer larger than or equal to a given number. Sign function: Returns only the sign of a number, as +1, −1 or 0. Absolute value: distance to the origin (zero point)

  6. Inequality (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Inequality_(mathematics)

    The notation a < b means that a is less than b. The notation a > b means that a is greater than b. In either case, a is not equal to b. These relations are known as strict inequalities, [1] meaning that a is strictly less than or strictly greater than b. Equality is excluded.

  7. Aaron Rodgers Reveals He Has a New Girlfriend: 'It's a Good ...

    www.aol.com/lifestyle/aaron-rodgers-reveals...

    Aaron Rodgers has a new romance in his life, the 41-year-old New York Jets quarterback revealed Monday.. On the Monday, Dec. 23 episode of the The Pat McAfee Show, Rodgers said he has a new ...

  8. No. 9 Duke's triumph over No. 2 Auburn can't salvage ... - AOL

    www.aol.com/sports/no-9-dukes-triumph-over...

    No. 9 Duke picked up its biggest win of the season on Wednesday, handing No. 2 Auburn its first loss. That was the extent of the good for the ACC.

  9. Microsoft Excel - Wikipedia

    en.wikipedia.org/wiki/Microsoft_Excel

    Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).