By J. Donald Monk
This booklet is inteded to be a self-contained creation to the entire set thought wanted by way of such a lot mathematicians. The method of set thought here's axiomatic. Logical symbolism is used, yet merely the place it truly is crucial, or the place it sort of feels to elucidate a scenario. Set conception can be in keeping with formal common sense, yet the following it truly is in line with intuitive common sense. We country all of the set-theoretical axioms on the begining , in Sec.1. The axiomatic method used is that of Kelley and Morse, expounded within the appendix of Kelley 1955.
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Extra resources for Introduction to Set Theory (International Series in Pure and Applied Mathematics)
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Since x = 3, no matter what y-coordinate is used, the corresponding x-coordinate always equals 3. Consequently, the graph of the equation x = 3 is a vertical line with x-intercept (3, 0) as shown in Figure 9. ■ SOLUTION x=3 x 5 (3, 0) (3, –1) ▲ Theorem As suggested by Example 4, we have the following result: Equation of a Vertical Line A vertical line is given by an equation of the form x؍a where (a, 0) is the x-intercept. EXAMPLE 5 Finding the Equation of a Vertical Line Find an equation for the vertical line containing the point (- 1, 6).
If an Army female who is 67 inches tall should weigh 139 pounds and an Army female who is 70 inches tall should weigh 151 pounds, find a linear equation that expresses recommended weight in terms of height. 115. 908 billion in 2008. (a) Assuming that the dollar amount of annual increase in total sales and other operating income will remain constant, find a linear equation expressing total sales and other operating income S for Chevron Corporation in terms of the time t in years. (b) Use this equation to predict total sales and other operating income for Chevron Corporation in the year 2011.
123. Can every line be written in slope–intercept form? Explain. y 124. Does every line have two distinct intercepts? Explain. Are x there lines that have no intercepts? Explain. 125. What can you say about two lines that have equal slopes and equal y-intercepts? 126. What can you say about two lines with the same x-intercept and the same y-intercept? Assume that the x-intercept is not (0, 0). 121. Which of the following equations might have the graph shown. ) (a) 2x + 3y = 6 (b) 2x - 3y = 6 (c) 3x + 4y = 12 (d) x - y = 1 (e) x - y = - 1 (f) y = - 2x + 1 1 (g) y = - x + 10 2 (h) y = x + 4 119.