Arithmetic
The expression for adding the numbers 1 and 2 is, in prefix notation, written "+ 1 2" rather than "1 + 2". In more complex expressions, the operators still precede their operands, but the operands may themselves be nontrivial expressions including operators of their own. For instance, the expression that would be written in conventional infix notation as
- (5 − 6) * 7
can be written in prefix as
- * (− 5 6) 7
Since the simple arithmetic operators are all binary (at least, in arithmetic contexts), any prefix representation thereof is unambiguous, and bracketing the prefix expression is unnecessary. As such, the previous expression can be further simplified to
- * − 5 6 7
The processing of the product is deferred until its two operands are available (i.e., 5 minus 6, and 7). As with any notation, the innermost expressions are evaluated first, but in prefix notation this "innermost-ness" can be conveyed by order rather than bracketing.
In the classical notation, the parentheses in the infix version were required, since moving them
- 5 − (6 * 7)
or simply removing them
- 5 − 6 * 7
would change the meaning and result of the overall expression, due to the precedence rule.
Similarly
- 5 − (6 * 7)
can be written in Polish notation as
- − 5 * 6 7
Read more about this topic: Polish Notation
Famous quotes containing the word arithmetic:
“‘Tis no extravagant arithmetic to say, that for every ten jokes,—thou hast got an hundred enemies; and till thou hast gone on, and raised a swarm of wasps about thine ears, and art half stung to death by them, thou wilt never be convinced it is so.”
—Laurence Sterne (1713–1768)
“Under the dominion of an idea, which possesses the minds of multitudes, as civil freedom, or the religious sentiment, the power of persons are no longer subjects of calculation. A nation of men unanimously bent on freedom, or conquest, can easily confound the arithmetic of statists, and achieve extravagant actions, out of all proportion to their means; as, the Greeks, the Saracens, the Swiss, the Americans, and the French have done.”
—Ralph Waldo Emerson (1803–1882)
“I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.”
—Gottlob Frege (1848–1925)