In mathematical proofs, which of the following are true? I : A theorem cannot be proved by example. II: Quantifiers are important. III: Never assume any hypothesis that is not explicitly stated in the theorem. A. I only B. III only C. I, II, III D. ...
where is a natural number, and is a predicate involving the ring operations of , the equality symbol , an arbitrary number of constants and free variables in , the quantifiers , boolean operators such as , and parentheses and colons, where the quantifiers are always understood to be over the...
There’s a lot more to say about this subject, such as the role of intuitionistic vs. classical logic, and the relationship between quantifiers and dependent types …however, I still don’t understand these deeper aspects of the subject very well, so I won’t say any more in this post....
So, Mean, Median, Mode - what exactly are they and how are they different from one another? We hear about them a lot, and three of them feel somehow related. However, each has a distinct role in helping us make sense of data sets and numbers more easily. While we won’t go into ...
If one really wants to deal with multiple values of objects simultaneously, one is encouraged to use the language of set theory and/or logical quantifiers to do so. However, the ability to allow expressions to become only partially specified is undeniably convenient, and also rather intuitive....