if and only if and
Following is a proof that the ordered pairs and are equal if and only if and .
If and , then .
Assume that and . Then . Thus, . Therefore, . Hence, and . Since it was also assumed that , it follows that and .
Finally, assume that and . Then . Note that . Thus, . It cannot be the case that (lest ). Thus, . Therefore, . Hence, . Note that . Since , it must be the case that . Thus, . Since , it must be the case that . It follows that and . ∎
|Title||if and only if and|
|Date of creation||2013-03-22 16:13:19|
|Last modified on||2013-03-22 16:13:19|
|Last modified by||Wkbj79 (1863)|