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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 this context, the terms string and number may be used interchangeably, since a number is actually a string of symbols, e.g. an English word (like the word "eleven" used in the paradox) while, on the other hand, it is possible to refer to any word with a number, e.g. by the number of its position in a given dictionary or by suitable encoding.
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.
Subtract the smaller number from the bigger number. If the result is not 6174, return to step 2 and repeat. This process, known as Kaprekar's routine , is guaranteed to reach a fixed point at the value 6174 in no more than 7 iterations, [ 4 ] at which point it will continue yielding that value ( 7641 – 1467 = 6174 ).
They have specific rules, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that satisfies the given conditions. Mathematical puzzles require mathematics to solve them.
Some theories consider "numeral" to be a synonym for "number" and assign all numbers (including ordinal numbers like "first") to a part of speech called "numerals". [ 1 ] [ 2 ] Numerals in the broad sense can also be analyzed as a noun ("three is a small number"), as a pronoun ("the two went to town"), or for a small number of words as an ...
There are several ways of coming up with a number, but actual cash value (ACV) is one of the most common valuation methods used in insurance. ACV is calculated using the car’s current market ...
The multi-sentence version of the liar paradox generalizes to any circular sequence of such statements (wherein the last statement asserts the truth/falsity of the first statement), provided there are an odd number of statements asserting the falsity of their successor; the following is a three-sentence version, with each statement asserting ...