# abide by / inequation holds

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#### a3mlord

##### Senior Member
For a given set of elements, should we say they they all abide by a given inequation or that a given inequation holds/holds true for all of them?

• #### entangledbank

##### Senior Member
Inequality, not inequation, and I'd say the inequality holds for all of them.

#### Edinburgher

##### Senior Member
I agree, 'abide by' doesn't work in this context, and it should be 'holds', not 'holds true'.

Actually, EB, 'inequation' sounds a bit iffy to me too, but apparently (according to Wikipedia, which is never wrong ), 'inequality' and 'inequation' both exist, and the distinction between them is the same as that between 'equality' (a relation between two quantities) and 'equation' (a statement that the relation holds). Is that distinction artificial too?

I don't recall coming across the term either, but it does appear in my Dictionary of Mathematical Sciences (German-English and English-German) (Herland; Ungar, New York, 1951, 2nd ed 1965).

#### entangledbank

##### Senior Member
I'm a mathematician and I've only ever seen 'inequality', not 'inequation', for this.
http://en.wikipedia.org/wiki/Inequality_(mathematics)
It sounds like someone's trying to keep an artificial distinction.

Edit. As I have to try and fix that broken link - and I find I can't edit my previous comment, perhaps because of it - I'll amplify my statement that it's an artificial distinction. Normally, in practice, we would say that these are all equations:

1 + 3 = 4
(x + y)^2 = x^2 + 2xy + y^2
x = 4

and likewise these are all inequalities:
3 < 4
d(x, z) <= d(x, y) + d(y, z)
x < 4
They may be identities, theorems, or problems, but they all have the same essential form, and in practice we don't need two words for the same thing.

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#### Edinburgher

##### Senior Member
I agree that it's artificial and not really found in practice, but nevertheless I find the distinction potentially useful.

Notice how at the very top of the wiki article to which you refer, it says Not to be confused with Inequation.
And yet http://en.wikipedia.org/wiki/Inequation comes with the caveat that the article "needs additional citations for verification."

Now where did I put that grain of salt?

#### a3mlord

##### Senior Member
Edinburgher in Computer Science, we always say inequation.

Can you please explain in which sense if "holds" different than "holds true"? I always thought they were exactly the same.

#### Myridon

##### Senior Member
Edinburgher in Computer Science, we always say inequation.
I stayed out of this because I lack two university courses of being a mathematician, but I do have a computer science degree, and I assure you that we (native-English-speaking computer scientists) do not say "inequation."

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#### a3mlord

##### Senior Member
VERY interesting. I'll definitely check this with my contacts in the US (both native and non-native speakers) teaching Computer Science and get back to you. I am sorry if I sound skeptical, but I've been both writing (means nothing in this case ) and reading "inequation" for a couple of years, in scientific papers. Now, we all know that scientific papers are written in the most universal language ever - bad english - but I am very curious about this and I want to investigate this further.

Thanks!

#### Forero

##### Senior Member
I am an American from the U.S., with a Bachelor of Science degree in Mathematics with a minor in Computer Science. I have worked 35 years as a mainframe systems programmer, and I have heard and read both inequality and inequation.

Logically you can say that an assertion is true, or that it holds, or that it holds true, or you can just make the assertion without mentioning "truth" or saying anything holds. In any of these cases, if the assertion is true, you are right; if it is false, you are wrong.

Inequality (noncount) is the opposite of equality. They are ideas, not assertions, so they don't "hold".

But an inequality (count) is, in common use, the same thing as an inequation, a formal assertion that two things are unequal, but the two terms are used differently in different books, papers, speeches, etc. Their use depends on what is convenient to the author in conveying an intended meaning.

The same thing happens with relationship and relation, gerundive and gerund. The distinction is greater in some circles than in others.

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#### Edinburgher

##### Senior Member
but I do have a computer science degree, and I assure you that we (native-English-speaking computer scientists) do not say "inequation."
I too have a CS degree (which was originally to have been in maths, but I switched half way through), and I have no recollection of coming across the term 'inequation' before now. It simply is common practice to refer to a solvable equation that happens to involve something other than an equals-sign as an inequality instead of an inequation (although technically the latter would be more logical).

If this 'new' term is creeping into the literature, it may simply be the result of non-native translations of papers into English from other languages. It may be relevant here that a3mlord gives his location as Germany (and I know that German does use the same ending for the words describing an equation and a "non-equation"). I don't know what Portuguese does for this; it may be a similar story.

#### a3mlord

##### Senior Member
Good point.

In Portuguese we have four different words for "Equation", "Inequation", "Equality" and "Inequality". They are "Equação", "Inequação", "Igualdade" and "Desigualade". The first two are only valid in the context of Maths. The others can be applied to everything and guess what... including in Mathematics, with the "same" meaning of "Equação/Inequação".

In German, however, they have only "Gleichung" and "Ungleichung", and they the former both for "equation" and "equality".

This another reason that leads me to believe that in English there are also four words. Maybe we can use them all in the context of Maths.

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