proof of alternative characterization of filter
First, suppose that is a filter. We shall show that, for any two elements and of , it is the case that if and only if and .
By the definition of filter, if and then . Since and is a filter, implies . Likewise, implies .
If and , then . By our hypothesis, .
The third defining property of a filter — If and then — is part of our hypothesis.
|Title||proof of alternative characterization of filter|
|Date of creation||2013-03-22 14:43:05|
|Last modified on||2013-03-22 14:43:05|
|Last modified by||rspuzio (6075)|