Talk:Term (logic)

Untitled section

why the TERM is the basic and indivisible element of an inference?— Preceding unsigned comment added by 112.210.145.60 (talk) 07:49, 24 July 2012‎ (UTC)

It isn’t. Why do you think so?—Emil J. 10:17, 24 July 2012 (UTC)

Variable arity predicates?

Has anyone heard of such things being useful in some logic(s)? I'm referring to [1] [2]. Tijfo098 (talk) 16:00, 26 November 2012 (UTC)

Apparently Quine considered such predicates to formalize ambiguity in natural languages [3]. Anyway, if this flavor is notable enough, it should be covered in the article on predicate (mathematical logic) rather than link to the weird article "multigrade operator"; a predicate models a relation not a function/operator. Tijfo098 (talk) 16:08, 26 November 2012 (UTC)

An example is given here. I suppose someone could create multigrade predicate. Tijfo098 (talk) 16:52, 26 November 2012 (UTC)

The catch is that you don't need such predicates in mathlogic. The reason to consider such constructs a single predicate is based on philosophy of language arguments. Tijfo098 (talk) 16:57, 26 November 2012 (UTC)

Some guys did consider predicates on strings seriously after Quine's proposal. Tijfo098 (talk) 01:53, 27 November 2012 (UTC)

Join with "Term_(mathematics)"?

I suggest to join this article with Term_(mathematics), as there is no difference between both notions. Jochen Burghardt (talk) 11:23, 18 May 2013 (UTC)

Jochen Burghardt (talk) 19:20, 12 June 2013 (UTC)

Untitled section 2

I believe this statement, "For example, in 6 + 3x − 2, 6, 3x, and −2 are all terms." is incorrect. The terms should be 6, 3x, and 2. Rationale is as follows -

-6x + 12 + 8x + 4. In this equation, no would argue that the terms are -6x, 12, 8x, and 4; and that the constants are 12 and 4.

3p + 2 +8p – 6 +5x. In this equation, the terms are 3p, 2, 8p, 6, and 5x. This is at odds with the example cited. Why should the term should be "6" and not "-6"?

1. In elementary formulas of the format “a – b”, the minus sign is an operator and the two terms are “a” and “b”, the “a” being the minuend and “b” being the subtrahend. 2. To change the sign of the subtrahend (thus inverting the operator) a multiplication is required, that being the product of the subtrahend and -1. The value of the subtrahend is changed by this step and the new term would then become “-b”.

If we apply the standard set by the example to the first formula, we would see that to maintain equivalence would require the following –

(a) (-1) * 6 + 12 + 8x + 4. This introduces a new term (-1) and a new operator (*).

(b) If we rewrite the first formula as 12 + 8x + 4 – 6x, we see that the associative property of addition has been applied to promote equivalence, essentially adding a predicate of (=) to make true: -6x + 12 + 8x + 4 = 12 + 8x + 4 – 6x. In either case, whether multiplying by -1 or applying the associative property, an operation has been performed.MrSteeb (talk) 12:37, 7 October 2014 (UTC)

Objection to language in "elementary mathematics"

Using "term" to mean "summand" is common not only in elementary mathematics, and not only for polynomials. I think most professional mathematicians would usually use the word "term" in the context of a series (even of much more complicated things than monomials). "Summand" is very unusual, and usually refers to something subtly different (the summand considered as a function of the index, rather than a particular individual term), and I have never seen "addend" in a research article. I suspect that this article was written by a logician that is so deeply embedded in their branch of mathematics that they never read research articles from other branches (which is of course fair) so assume that all other professional mathematicians use the word "term" like they do (which is not fair).

So I suggest these modifications:

• Most importantly, include this meaning in the lead section. Most links to this article are almost certainly for this usage, so it's very confusing that it's not in the lead.
• Remove references to "elementary mathematics". Perhaps rename the first section to something like "terms in a series".
• Acknowledge that this is not the technically correct use of the word, but that it is the common usage outside of mathematical logic.
• Remove the requirement that the series be a polynomial.
• Remove the obscure list of terms (minuend and subtrahend!?) from the first section.
• Add a couple of examples in the first section, and contrast with the word "factor". A good one would be something like

(a+b)(c+d)=ac+ad+bc+bd

where the left hand side has two factors each containing two terms (e.g. the first factor a+b has terms a and b) and the right hand side has four terms each containing two factors (e.g. the first term ac has factors a and c). Then mention some standard series such as geometric series, which (quoting the first sentence of that article) "is a series with a constant ratio between successive terms". Another good example would be the Fourier series, where each term is a trigonometric function.

Quietbritishjim (talk) 09:13, 24 October 2014 (UTC)

This section is very incorrect. I've even bought the referenced book because it was so incorrect I had to see what type of person would publish this information. Turns out the book is correct, and nothing mentioned in this section is written in the book.

I would suggest replacing entire "elementary math" section with "In mathematics, terms are expressions that are bounded by plus signs." Factchecker170 (talk) 21:19, 18 April 2019 (UTC)

After no response in talk for a week I updated the section to match the referenced source. This section was then changed again, but without a new reference, the new text does not match the reference. I've undone the change pending discussion and/or identifying of a source to validate the change. Factchecker170 (talk) 18:42, 30 April 2019 (UTC)

@Factchecker170: I have to apologize for reverting your edit without discussing here first. Unfortunately, I cannot access the book you cited. However, I'm still convinced that my reasons given in the edit summary are correct: "t" is a term in "1+t" and in "1-t" (you wouldn't challenge that, would you?), although it is nowhere "bounded by plus signs". So obviously Schwartzman should be taken with a grain of salt , and I thought (and still think) I added it. I reverted your removal of "elementary" because it is common understanding in mathematics that names don't matter (a fairly good explanation can be found at Foundations of geometry#Axiomatic systems, citing Hilbert's famous remark). The meaning of "term" as being related somehow to the name "+" is found only in elementary school, and in applied sciences when they employ e.g. real or complex numbers. - Jochen Burghardt (talk) 07:42, 2 May 2019 (UTC)

Whether t is a term in 1-t is contested. -t could be considered the term. However rereading the source I don't see a discrepancy with including "or negative signs", (am I allowed to just directly quote the book in here? Is there a place I can upload a screenshot for others reference? I'm new to editing and don't quite grasp all the regulations yet). I bought my copy on amazon for about 8 bucks, I was not the original author that included it as a reference, I just noticed that the previous version was did not match my background knowledge and was curious about the exact language of the source.

I do disagree with your assertion that terms being related to "+" are an elementary school concept. I can agree with "elementary" as in basic, but in US education the term "term" is first assessed in the 6th grade which is often placed as secondary education in middle school. Additionally the concept of terms is very important throughout algebra. Factchecker170 (talk) 19:55, 2 May 2019 (UTC)

I think, literally quoting a few sentences is ok here. In another discussion, I uploaded a photo of a book page under a "fair use" rationale, and learned that it will be deleted after about a week, anyway. As for the "1-t" example: I understand "X is bounded by Y signs" to mean "X" should have a "Y" both left and right to it. Other examples where my intuitive understanding of "term" (and I guess, yours, too) deviates from the literal definition are "1+t<u" and "x-(t+2)".

I have to admit that, when I used "elementary", I didn't think too much about its possible meanings. Also, I am not familiar with the US education system. If the word "elementary" can be misleading, what about "applied" instead? This would also cover e.g. physicists' and engineers' idioms like "in this expression we can neglect the term x^-3 because it is very small". Would that be ok for you? - Jochen Burghardt (talk) 20:34, 2 May 2019 (UTC)

"bounded" was specifically used in the book, but I see your point. I'm out of town for the weekend, how about on Monday I post the exact section from the book, and we can continue from there? Factchecker170 (talk) 15:53, 3 May 2019 (UTC)

In the next week, I may be offline for a few days. If you intend to upload a non-free image, you'd do me a favor if you defer that a little bit. - Jochen Burghardt (talk) 18:58, 4 May 2019 (UTC)

I'm online again. Thanks for waiting. - Jochen Burghardt (talk) 19:39, 12 May 2019 (UTC)