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The consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example, the sentence "a free module is a module that has a basis" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of basis, module, and free module.
For example, squares (resp. triangles) have 4 sides (resp. 3 sides); or compact (resp. Lindelöf) spaces are ones where every open cover has a finite (resp. countable) open subcover. sharp Often, a mathematical theorem will establish constraints on the behavior of some object; for example, a function will be shown to have an upper or lower bound.
Will Rogers phenomenon: The mathematical concept of an average, whether defined as the mean or median, leads to apparently paradoxical results—for example, it is possible that moving an entry from an encyclopedia to a dictionary would increase the average entry length on both books.
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...
Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).
Some of the related mathematical skills necessary for solving word problems are mathematical vocabulary and reading comprehension. This can again be connected to the example above. With an understanding of the word "spent" and the concept of subtraction, it can be deduced that this word problem is relating the two. [2]
In mathematical logic, a sentence (or closed formula) [1] of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition , something that must be true or false.
A valid number sentence that is true: 83 + 19 = 102. A valid number sentence that is false: 1 + 1 = 3. A valid number sentence using a 'less than' symbol: 3 + 6 < 10. A valid number sentence using a 'more than' symbol: 3 + 9 > 11. An example from a lesson plan: [6] Some students will use a direct computational approach.