English Translation of Italian Lecture Notes: Equations & Solutions

[FranzDiCoccio]

TL;DR Summary

I'd like to know a few terms about equations. I do not have an English textbook. I looked online but I still have some doubts

Hi,
I am looking at some lecture notes in Italian, and I'm wondering about the correct English translation for some terms.
I am afraid that in some cases the "literal" translation would sound weird.
I looked online but I still have some doubts. In some cases I was not able to find a satisfactory "translation", and I suspect that it might not exist (not because of a lack of terms, but probably because there is no real need to bother for a specific definition).

So, in the notes I'm looking at, individual equations are classified based on the number of their solutions. The terms are basically the same as for linear systems.

An equation with no solutions is called "impossible equation" (literal translation). For instance $x+3=x-7$ or $x^2+1=0,\;x\in\mathbb{R}$.
I think the correct English term would be "inconsistent equation" or perhaps "contradiction".

An equation with a finite set of solutions is called "determinate equation" (literal translation). For instance $2x+3=x-7$ or $x^2-2=0$.
Here the correct term seems to be "conditional equation", but I'm not sure. I only found examples involving linear equations.

An equation with infinitely many solutions is called an "indeterminate equation" (literal translation). For instance. e.g. $6x+2=2(3x+1)$, which is also an "identity", and $x+y=2$). This might be a "false friend" since, as far as I understand, in English an indeterminate equation has more than one solution, but not necessarily infinite.
I did not find a single term for this situation, which is always referred to as "an equation with infinitely many solutions".

Can someone help me with these definitions?

 

[PeroK]

An equation with no solutions

An equation with a finite set of solutions

An equation with infinitely many solutions

In all three cases we would just say how many solutions an equation has. There is no single adjective as an alternative. For example we would say the equation $x^2+1=0$ has no real solutions.

 

[fresh_42]

Here are some translation tricks:
https://www.physicsforums.com/threads/tips-and-tricks-for-any-occasion.1016388/

 

[FranzDiCoccio]

Hi fresh_42,
thanks for the tip. I usually try that. Or better, I look for definitions in English and match them to the Italian ones.
The method you suggest won't always work. Wikipedia pages in different languages may have pretty different structures. Often they are not simple translations of the same text.
In this case, the Italian page is much shorter than the English one, but contains a paragraph "nomenclatura" discussing the definitions I gave above.
I cannot find anything relevant in the English version of the page.

 

[FactChecker]

If you find English adjectives for those cases, they will not be well recognized by others. It is best to follow @PeroK's advice.

 

[PeroK]

I cannot find anything relevant in the English version of the page.

That's because there isn't anything.

 

[FranzDiCoccio]

In all three cases we would just say how many solutions an equation has. There is no single adjective as an alternative. For example we would say the equation $x^2+1=0$ has no real solutions.

I suspected that English might not have/need those definition, but I was not sure.
For instance, I believe you have definitions for similar concepts in the context of linear systems (consistent, inconsistent, dependent).

If you find English adjectives for those cases, they will not be well recognized by others. It is best to follow @PeroK's advice.

I see what you mean. My only worry is that the notes I'm looking at refer to a "crash course" that is taught in an Italian University and is meant to bring foreign students "up to speed".
I'll have to make sure that the subsequent courses use consistent definitions (or, in this case, do not use any single word to define those concepts).

 

[PeroK]

I would say you have to learn the correct terminology from English language sources. It's not a good idea to translate individual terms willy-nilly. There's a good English expression for you!

 

[FranzDiCoccio]

I would say you have to learn from English language sources. It's not a good idea to translate individual terms willy-nilly. There's a good English expression for you!

Of course, that's why I've asked in the first place.
Thanks

 

[fresh_42]

Hi fresh_42,
thanks for the tip. I usually try that. Or better, I look for definitions in English and match them to the Italian ones.
The method you suggest won't always work.

You must be a bit more creative. E.g.
https://it.wikipedia.org/wiki/Equazione_di_quinto_grado -->
https://it.wikipedia.org/wiki/Teorema_di_Abel-Ruffini -->
"la cui soluzione non può essere espressa tramite radicali e un esempio"
https://en.wikipedia.org/wiki/Abel–Ruffini_theorem
"equations of degree five and higher that cannot be solved by radicals"

 

[FactChecker]

I see what you mean. My only worry is that the notes I'm looking at refer to a "crash course" that is taught in an Italian University and is meant to bring foreign students "up to speed".
I'll have to make sure that the subsequent courses use consistent definitions (or, in this case, do not use any single word to define those concepts).

You were smart to ask. Every aspect of the English language is full of inconsistencies. Mathematics terms are no exception. It is always best to define your terms in the text that they appear in or else there will be many arguments about their meaning.

 

[FranzDiCoccio]

You must be a bit more creative. E.g.
https://it.wikipedia.org/wiki/Equazione_di_quinto_grado -->
https://it.wikipedia.org/wiki/Teorema_di_Abel-Ruffini -->
"la cui soluzione non può essere espressa tramite radicali e un esempio"
https://en.wikipedia.org/wiki/Abel–Ruffini_theorem
"equations of degree five and higher that cannot be solved by radicals"

Thanks for your help.
I usually find a translation, when it exists, often using the method you suggest.

The point here is the lack of a translation, though.

As I mention in the O.P., since in this case I could not find one, I suspected that there wasn't any.
Your examples above sort of confirm this, since none of them refers to the concepts in my question.

I asked anyway just to confirm my suspect.

After all English has many words that shorten long definitions. Consistent, inconsistent and dependent are quite relevant examples in the context of linear systems (they express basically the same properties I'm concerned with, only for systems instead of single equations).

Also monomial, binomial, trinomial etc can be expressed in many words, and yet a single word is used.

Apparently English has no word for an equation with an infinite number of solutions, or perhaps such word exists but it is not widely used, and would not be recognized anyway (btw the "guess" in my OP for an equation that has no solution comes from here).