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In mathematical logic, a sentence is a formula with no free variables; therefore, a sentence is either true or false in a given structure. For example is not a sentence, because of the presence of the free variable y; it will be true in the structure of the real numbers if y = 2, but not if y = − 2. On the other hand is a sentence, and is false in the real numbers. Wikipedia Logo File links The following pages link to this file: Talk:Amino acid Australian Army Boxing Bioterrorism Brick Broadway (Manhattan) Geography of Canada Transportation in Chile Confucius Colorado Rockies Origins beliefs Democracy Document Type Definition Equuleus East Slavic languages Flanders Fifth Monarchy Men Grenada Geyser Harry Potter Information explosion... In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation for a place or places in an expression, into which some definite substitution may take place, or with respect to which some operation (summation or quantification, to give two... In mathematics, a structure on a set is some additional mathematical objects that, loosely speaking, attach to the set, making it easier to visualize or work with. ... In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. ...