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Introduction to HyperReals
Introduction to HyperReals

...  The set R of real numbers is a subset of the set R* of hyperreal numbers.  The order relation <* on R* is an extension of the order < on R.  There is a hyperreal number  such that 0 <*  and  <* r for each positive real number r.  For each real function f there is a given hyperreal function f ...
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... Here, the (+) above a portion of the number line indicates f (x) > 0 for those values of x; the (−) indicates f (x) < 0 there. The numbers labeled on the number line are the zeros of f , so we place 0 above them. We see at once that the solution to f (x) < 0 is (−2, 3). Our next goal is to establish ...
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... F (β, t, L, U); β, t, L, U are given integers. This is a collection of all floating-point numbers in base β, with a mantissa that has exactly t digits (i.e., s = t). Also, the exponent is in between the integers L and U, or L ≤ e ≤ U. Therefore, F (β, t, L, U) contains all floating-point numbers of ...
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... To divide decimal numbers, the problem must be in long division form. • To begin long division, the divisor must be a whole number. Divide decimal numbers. Step #1: Change the problem into long division form, if needed. Step #2: Move the decimal point in the divisor to change it to a whole number, i ...
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Elementary mathematics



Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. The most basic topics in elementary mathematics are arithmetic and geometry. Beginning in the last decades of the 20th century, there has been an increased emphasis on problem solving. Elementary mathematics is used in everyday life in such activities as making change, cooking, buying and selling stock, and gambling. It is also an essential first step on the path to understanding science.In secondary school, the main topics in elementary mathematics are algebra and trigonometry. Calculus, even though it is often taught to advanced secondary school students, is usually considered college level mathematics.
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