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January 5th, 2017, 10:29 AM   #1
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Nomenclature

Just would like some help on getting my understanding on the right footing on certain terms.

Math can be displayed in its raw form in these methods:

equations
A balanced expression; such that, it has two expressions on each side.

functions
I would use algorithm to describe this term, because it is essentially an expression with an input. It has its own rules under geometry/calculus on how it must behave.
- algorithm (synonym minus the constraints a function has)

formulas
almost like a functions except with more than one input. Granted a function can have more than one variable, however, the 'function' still obeys the input output behavior designated by its definition.
- expression (synonym?)
- polynomials (synonym?)





Anyone critique or inform me on any of those or those I have left out. Much appreciated


-Buffalo
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January 5th, 2017, 11:51 AM   #2
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Quote:
Originally Posted by Buffalo View Post
equations
A balanced expression; such that, it has two expressions on each side.
Surely there is only one expression on each side of the equal sign. An equation is a statement asserting that two expressions represent the the same mathematical object.

Quote:
Originally Posted by Buffalo View Post
functions
I would use algorithm to describe this term, because it is essentially an expression with an input. It has its own rules under geometry/calculus on how it must behave.
- algorithm (synonym minus the constraints a function has)
Some functions can be expressed by algorithms. Most can't. For example if we take functions from $\mathbb N\rightarrow \mathbb N$ there are uncountably many such functions, but there are only countably many expressions.

As a specific example of a function that has no algorithm, suppose we flip a fair coin one time for each natural number. Most of the time the resulting bitstring will be random; that is, not compressible to a smaller string. That's a function that has no algorithm.

Quote:
Originally Posted by Buffalo View Post
formulas
almost like a functions except with more than one input. Granted a function can have more than one variable, however, the 'function' still obeys the input output behavior designated by its definition.
- expression (synonym?)
- polynomials (synonym?)
Formula is more a term from logic, as in well-formed formula. It's a syntactic entity composed of symbols from some formal alphabet. But that terminology is not used consistently in math. For example we have the "quadratic formula" that gives the solution to a quadratic equation.

Last edited by Maschke; January 5th, 2017 at 12:18 PM.
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