Tom Kelliher, MA 190
Feb. 6, 2008
Example: For every pair of real numbers, their sum is a real number.
proved := true; for x := each element in its domain confirmed := true; for y := each element in its domain if P(x, y) == false confirmed := false; break; if confirmed == false proved := false; break; return proved;
Example: For every integer, , there is an integer, , such that .
proved := true; for x := each element in its domain confirmed := false; for y := each element in its domain if P(x, y) == true; confirmed := true break; if confirmed == false proved := false; break; return proved;
Example: There is a real number that when multiplied by any real number, , results in a product of .
proved := false; for x := each element in its domain confirmed := true; for y := each element in its domain if P(x, y) == false confirmed := false; break; if confirmed == true proved := true; break; return proved;
Example: There are two integers whose product is 12.
proved := false; for x := each element in its domain confirmed := false; for y := each element in its domain if P(x, y) == true confirmed := true; break; if confirmed == true proved := true; break; return proved;