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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.
An expression is often used to define a function, by taking the variables to be arguments, or inputs, of the function, and assigning the output to be the evaluation of the resulting expression. [5] For example, x ↦ x 2 + 1 {\displaystyle x\mapsto x^{2}+1} and f ( x ) = x 2 + 1 {\displaystyle f(x)=x^{2}+1} define the function that associates ...
A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values : as the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.
In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (x) that is not defined or specified (thus being a free variable), which leaves the statement undetermined.
For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243. The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3, or 3 raised to the 5th power. The word "raised" is usually omitted, and sometimes "power" as well, so 3 5 can be simply read "3 to the 5th", or "3 to the 5".
The sentence can be read as "Reginam occidere nolite, timere bonum est, si omnes consentiunt, ego non. Contradico. " ("don't kill the Queen, it is good to be afraid, even if all agree I do not. I object."), or the opposite meaning " Reginam occidere nolite timere, bonum est; si omnes consentiunt ego non contradico.
The declarative sentence is the most common kind of sentence, and can be considered the default form: when a language forms a question or a command, it will be a modification of the declarative. A declarative states an idea (either objectively or subjectively on the part of the speaker; and may be either true or false) for the purpose of ...
In mathematics, the exterior algebra or Grassmann algebra of a vector space is an associative algebra that contains , which has a product, called exterior product or wedge product and denoted with , such that = for every vector in .
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