...(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...

...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...

...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)...

...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...

...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...

...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,...