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Hyperbole is often used for emphasis or effect. In casual speech, it functions as an intensifier: [5] [3] saying "the bag weighed a ton" [6] simply means that the bag was extremely heavy. [7] The rhetorical device may be used for serious or ironic or comic effects. [8] Understanding hyperbole and its use in context can help understand the ...
Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory.
Exaggeration is the representation of something as more extreme or dramatic than it is, intentionally or unintentionally. It can be a rhetorical device or figure of speech, used to evoke strong feelings or to create a strong impression.
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.
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 instance, if the one solving the math word problem has a limited understanding of the language (English, Spanish, etc.) they are more likely to not understand what the problem is even asking. In Example 1 (above), if one does not comprehend the definition of the word "spent," they will misunderstand the entire purpose of the word problem.
For example, in every logical system capable of expressing the Peano axioms, the Gödel sentence holds for the natural numbers but cannot be proved. Here a logical system is said to be effectively given if it is possible to decide, given any formula in the language of the system, whether the formula is an axiom, and one which can express the ...
For example, "one million" is clearly definite, but "a million" could be used to mean either a definite (she has a million followers now) or an indefinite value (she signed what felt like a million papers). The title The Book of One Thousand and One Nights (lit. "a thousand nights and one night") impiles a large number of nights. [22]