Abstract
An introduction to analysis usually begins with a study of properties of ℝ, the set of real numbers. It will be assumed that you know something about them. More specifically, it is assumed that you realize that
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(i)
they form a field (which means that you can add, multiply, subtract and divide in the usual way),and
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(ii)
they are (totally) ordered (i.e., for any two numbers a, b ∈ ℝ, either a < b, a = b, or a> b) and a ≥ b if and only if a - b ≥ 0. Note that a < b and 0 < c imply ac < bc; a ≤ b imply a + c ≤ b + c for any c ∈ ℝ; 0 < 1 and - 1 < 0.
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© 1997 Springer Science+Business Media New York
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Taylor, J.C. (1997). Probability Spaces. In: An Introduction to Measure and Probability. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0659-0_1
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DOI: https://doi.org/10.1007/978-1-4612-0659-0_1
Publisher Name: Springer, New York, NY
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