- #1

FranzDiCoccio

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- 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?

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?