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2. Number sentence - Wikipedia

   en.wikipedia.org/wiki/Number_sentence

   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.

3. Sentence (mathematical logic) - Wikipedia

   en.wikipedia.org/wiki/Sentence_(mathematical_logic)

   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.

4. Mathematical proof - Wikipedia

   en.wikipedia.org/wiki/Mathematical_proof

   For example, direct proof can be used to prove that the sum of two even integers is always even: Consider two even integers x and y. Since they are even, they can be written as x = 2a and y = 2b, respectively, for some integers a and b. Then the sum is x + y = 2a + 2b = 2(a+b). Therefore x+y has 2 as a factor and, by definition, is even. Hence ...

5. Well-formed formula - Wikipedia

   en.wikipedia.org/wiki/Well-formed_formula

   A closed formula, also ground formula or sentence, is a formula in which there are no free occurrences of any variable. If A is a formula of a first-order language in which the variables v 1 , …, v n have free occurrences, then A preceded by ∀ v 1 ⋯ ∀ v n is a universal closure of A .

6. Glossary of mathematical symbols - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_mathematical...

   In this section, the symbols that are listed are used as some sorts of punctuation marks in mathematical reasoning, or as abbreviations of natural language phrases. They are generally not used inside a formula. Some were used in classical logic for indicating the logical dependence between sentences written in plain language. Except for the ...

7. Logical consequence - Wikipedia

   en.wikipedia.org/wiki/Logical_consequence

   Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. [1] A sentence is said to be a logical consequence of a set of sentences, for a given language , if and only if , using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must ...