Exact definition of "expression"

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onesun0000

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What I learned about the definition of an expression is that it is a combination of numbers, symbols and operators to show a value. If this is the definition of an expression, is a term (either a constant or a variable with coefficient equal to, less than or greater than 1) not consider an expression?
 
onesun0000 said:
What I learned about the definition of an expression is that it is a combination of numbers, symbols and operators to show a value. If this is the definition of an expression, is a term (either a constant or a variable with coefficient equal to, less than or greater than 1) not consider an expression?
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I would say an expression is a combination of numbers, symbols AND/OR operators.
So yes
5 is an expression (albeit a trivial one)
2n is an expression (although the multiplication sign is not included, it is implied)
 
A term is an expression.

A term is one part of an addition, multiplication (or other mathematical operator).

An expression is not necessarily a term, for example "2n" on its own is not a term because its value is not used as input to a "+", "*", "/" etc. However, in the context of "2n + 1" then "2n" is both a term and an expression.
 
Cubist said:
A term is an expression.
Yes it is.

A term is one part of an addition, multiplication (or other mathematical operator).
No. A term is one part of an addition or subtraction. Terms in an expression are separated by + or - signs.
In the expression 2n + 6, both 2n and 6 are terms.
(In the expression 2n, 2 and n are factors not terms.)

An expression is not necessarily a term, for example "2n" on its own is not a term because its value is not used as input to a "+", "*", "/" etc. However, in the context of "2n + 1" then "2n" is both a term and an expression.
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see comments in red
 
I disagree slightly with the cat's definition. Here is mine (which probably does not differ materially from any feline intention.)

In elementary algebra, an expression denotes a number and is usually presented as a numeral, or a pronumeral, or a combination of simpler expressions that are joined by implicit or explicit symbols denoting mathematical operations and may be supplemented by grouping symbols. If an expression contains no pronumerals, it is an arithmetic expression. If an expression contains at least one pronumeral, it is an algebraic expression.

This definition begs the question of what is a pronumeral.

A pronumeral is a symbol (usually a letter from the Latin or Greek alphabets) that denotes a number that has not yet been specified or determined. Unlike a numeral, which always represents the same number, a pronumeral represents the same number only in the context of a given problem or discussion.
 
Computer scientist here.

An expression is one or more tokens that can be evaluated for use in an operation.
  • [MATH]5[/MATH] is an expression, as its evaluation is its own value.
  • [MATH]5+x[/MATH] is an expression that contains an operation (addition).
  • [MATH]y = 5+x[/MATH] is typically not an expression because it cannot be evaluated: it is a description of a relationship.
In a computer science context, [MATH]y = 5+x[/MATH] can actually be an expression, where the [MATH]=[/MATH] operator performs a test for decision making, but this is not a common use in mathematics outside of piecewise functions.

As an aside, many languages derived from C will even produce a result from an assignment operation, which can be used as part of a larger expression:
C: 
int a, b, c = 5;
a = (b = c * 3) + 2;
/* a == 17, b == 15 */
 
Cubist said:
Actually a factor is a term.

In the expression 2n + 6, both 2n and 6 are addends, terms, and expressions.

See https://simple.wikipedia.org/wiki/Term_(mathematics)
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I have never heard of "multiplicative terms". The correct name is "factors".
I agree that 2n and 6 are addends, terms and expressions.
Within 2n, the 2 and the n are factors, not terms - unless you call them "multiplicative terms".
 
@onesun0000 I'll bet you are more confused by the term term now (sorry I had to do that :))

There seems to be some disagreement here so I recommend that you ask your teacher. After all they will probably be marking any tests that you might have on this topic!
 
A term is separated by + and - signs which are not inside parentheses.

Here is the best way to list the terms of an expression. Every time you see a + or - sign which is NOT inside parentheses then replace it with a comma. The commas will separate the expression into items.

Example: 3x - 5 + 6(x+1) - 11y + 4(x+3y). So the terms are 3x, 5, 6(x+1), 11y and 4(x+3y)
 
Harry_the_cat said:
see comments in red
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Cubist said:
A term is an expression.
Yes it is.

A term is one part of an addition, multiplication (or other mathematical operator).
No. A term is one part of an addition or subtraction. Terms in an expression are separated by + or - signs.
In the expression 2n + 6, both 2n and 6 are terms.
(In the expression 2n, 2 and n are factors not terms.)

An expression is not necessarily a term, for example "2n" on its own is not a term because its value is not used as input to a "+", "*", "/" etc. However, in the context of "2n + 1" then "2n" is both a term and an expression.
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see comments in red
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Since we are grading people I am taking out my red pen as well.
You said "No. A term is one part of an addition or subtraction. Terms in an expression are separated by + or - signs."
I disagree with you saying + OR - signs. It should be + and- signs.[/QUOTE]
 
Jomo said:
Since we are grading people I am taking out my red pen as well.
You said "No. A term is one part of an addition or subtraction. Terms in an expression are separated by + or - signs."
I disagree with you saying + OR - signs. It should be + and- signs.
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[/QUOTE]
No I disagree.
If terms are separated by + AND - signs, then in a+b, a and b aren't terms (by your definition). By your defn, you would have to have a+-b or a-+b. That's rubbish and you would be sent to the corner if Denis was still among us.
 
Perhaps the wikipedia page where I sourced that information is incorrect, since there are now two people who disagree with it. I don't consider myself an authority which is why I looked this up on the aforementioned page before replying to the OP, and why I quoted the source. I guess the reference book cited on that page may have been misquoted or could be wrong. If anyone can recommend a definitive source of mathematical terminology then I'd be grateful, if such a thing exists?

To help the OP, it seems to me that everyone agrees that two or more things (lol) multiplied together can be called "factors" or "expressions" - so it is probably best sticking to those words. Maybe they can be called "multiplicands" too?

Also for clarity it might be worth pointing out that the words "factor" and "term" (in the Harry_the_cat and Jomo sense) just give an indication of the placement (or role) of a smaller expression within a larger expression. The words say nothing about the content of the smaller expression that they refer to. So, for example, when expanding brackets (a+b)*c -> a*c + b*c the "terms a and b" become "factors a and b", even though a and b themselves remain unchanged.
 
For those interested in the meaning of the word "term" I did some more research by Googling "encyclopedia of mathematical terms". The first page of results led to the following...

http://www.allmathwords.org/en/t/term.html

http://mathworld.wolfram.com/Term.html

https://www.encyclopediaofmath.org/index.php/Term

The top link most strongly agrees with Harry_the_cat and Jomo, but then goes on to imply that each term must be part of a polynomial (see * below)

The second link initially drops the "must be separated by + or - signs", and instead says that something raised to a power is a term. This implies that the name "term" can be applied to such an expression regardless of its position within a larger expression. But it then goes on to state "also used commonly to mean a summand of a polynomial". The word "summand" impies the presence of a + or - BUT restricts the use of the word "term" to be within the context of a polynomial (see * below)

The third link is very blasé implying that any "object" or "expression" can be called a term.

*- Not all expressions with + or - are polynomials (lol, or are they?). Example "cos(x) + abs(x) + floor(x*2)".

--

This reinforces my advice to OP that it is probably best to avoid using the word "term". If you can't avoid it then use the definition that your teacher (the one who marks your test) gives you!
 
to everyone

Thanks for the help. To be honest, I get a little bit more confused now. Maybe I should stick with what I learned from school (for now). Because eventually, I'll learn those higher degree of definitions. Thanks again...
 
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