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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 ...
Every normal function f has arbitrarily large fixed points; see the fixed-point lemma for normal functions for a proof. One can create a normal function f ′ : Ord → Ord, called the derivative of f, such that f ′(α) is the α-th fixed point of f. [2] For a hierarchy of normal functions, see Veblen functions.
In documentation and instructional design, tutorials are teaching-level documents that help the learner progress in skill and confidence. [7] Tutorials can take the form of a screen recording (), a written document (either online or downloadable), interactive tutorial, or an audio file, where a person will give step by step instructions on how to do something.
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).
In number theory, a normal order of an arithmetic function is some simpler or better-understood function which "usually" takes the same or closely approximate values. Let f be a function on the natural numbers. We say that g is a normal order of f if for every ε > 0, the inequalities
A fixed point of a normal function is an ordinal such that () =. The fixed point lemma states that the class of fixed points of any normal function is nonempty and in fact is unbounded: given any ordinal α {\displaystyle \alpha } , there exists an ordinal β {\displaystyle \beta } such that β ≥ α {\displaystyle \beta \geq \alpha } and f ...