In fact, two ordered pairs (a, b) and (c, d) are equal if and only if a = c and b = d. Definition The Cartesian product of set A with set B, written A x B and read "A cross B," is the set of all ordered pairs (a, b), where a £ A and b G B. Difference Algebra - Page 2by Alexander Levin - 2008 - 521 pagesLimited preview - About this book
| Emil G. Milewski - Mathematics - 1998 - 932 pages
...(3) and the unit element (1,0) (a,b) • (1,0) = (a-0, 0+b) = (a,b). (4) Two pairs (a,b) and (c,d) are equal if, and only if, a = с and b = d. A one-to-one correspondence can be established between all the pairs of the form (a,0) and the real numbers... | |
| Daniel Pedoe - Mathematics - 1988 - 468 pages
...introduce complex numbers as ordered pairs (a, b) of real numbers, and say that two complex numbers (a, b) and (c , d) are equal if and only if a = c and b = d. This is sometimes called : 'equating the real and imaginary parts of the two sides of... | |
| John F. Lucas - Mathematics - 1990 - 400 pages
...from B. The Cartesian product is denoted AXB (see Section 4.1). AXB = {(a, b)\ae A and be B} Also, two ordered pairs (a, b) and (c, d) are equal if and only if they are equal componentwise. That is, (a, b) = (c, d) » (a = c and b = d). (a) If n(A) = 5 and n(B)... | |
| B S Vatssa - Algebra - 1999 - 384 pages
...1.15: The ordered pairs of two elements a and b is denned by (a,b)={ (a, b}, {a} }. THEOREM 1.16: The ordered pairs (a, b) and (c, d) are equal if, and only if,a = c and b = d. Proof. If a = с and b = d, then {a} - {c} and [a, b] = [c, d], and consequently... | |
| Donald G. Newnan - Engineering - 2004 - 738 pages
...French (Exhibit 3). Exhibit 2 ¿and F, Product Sets An ordered pair of elements a and b is denoted by (a, b). Two ordered pairs (a, b) and (c, d) are equal only if a = c and b = d. For example, the ordered pairs (3, 4) and (4, 3) are different. The product... | |
| Charalambos A. Charalambides - Mathematics - 2005 - 440 pages
...as the second is called an ordered pair and is denoted by (a, b). According to this definition two pairs (a, b) and (c, d) are equal if and only if a = с and b = d. The concept of an ordered n-tuple (cii, 02, . . . , an) can be inductively defined as follows. Thus,... | |
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