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Math Definitions: Introduction to Numbers
Math Definitions: Introduction to Numbers

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... For instance, consider N iterations s0 , ..., sN of the baker’s transformation, perturbed by a sequence p0 , p1 , ..., such that for all i, |pi | ≤ ε and si is between 0 and 1. Then it is easy to prove, by decreasing induction on i, that for all i, there exists a element s0i , such that |s0i − si | ...
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HOMEWORK 11.1 #`s 1-9

... Some problems have more than one case. One way to solve such problems is to establish cases that together cover all of the possibilities. Calculate the number of arrangements for each case and then add the values for all cases to obtain the total number of arrangements. e.g. Determine the number of ...
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Positional notation

Positional notation or place-value notation is a method of representing or encoding numbers. Positional notation is distinguished from other notations (such as Roman numerals) for its use of the same symbol for the different orders of magnitude (for example, the ""ones place"", ""tens place"", ""hundreds place""). This greatly simplified arithmetic leading to the rapid spread of the notation across the world.With the use of a radix point (decimal point in base-10), the notation can be extended to include fractions and the numeric expansions of real numbers. The Babylonian numeral system, base-60, was the first positional system developed, and is still used today to count time and angles. The Hindu–Arabic numeral system, base-10, is the most commonly used system in the world today for most calculations.
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