5

Is "first member" or "second member" proper modern mathematical English to refer to the left-hand side (LHS) or right-hand side (RHS) of an equation, respectively?

Geremia
  • 2,405
  • 1
    Never heard that term (native English speaker, math PhD student). Generally we avoid writing multiple equals signs on the same line anyway, preferring to start a new line if we have more than two things that we want to say are the same. This possibly combined with equation numbering makes it easy to refer to the left or right side of any given equation even in a chain of equations. – Ian May 23 '18 at 00:32
  • @Ian It's common in French mathematical writing, which is why I asked. They don't say "left-hand side" or "right-hand side" of an equation, but "first member" or "second member" of the equation. – Geremia May 23 '18 at 00:36
  • 1
    Not surprised to hear of such a difference, but yeah, you will confuse English speakers if you say that. – Ian May 23 '18 at 00:37
  • @Geremia We do, but this doesn't mean that it is common in French mathematical writing to have several $=$ signs in a row. There is a first member and a second member and this is it. – Arnaud Mortier May 23 '18 at 00:38
  • @ArnaudMortier OK, so in English, "member" can mean "side of an equation"? – Geremia May 23 '18 at 00:41
  • @Geremia I've never heard it used in this sense. However, if you type in "member of the equation" into Google you will get some results. Then again they may be old, and they may be by non-native writers. – Arnaud Mortier May 23 '18 at 00:44
  • I've never heard this terminology before but mathematics is flexible. This is why it's important to define what you mean in presentations and papers. @ArnaudMortier does quite a lovely job of showing how you could introduce this in a paper naturally. He spells out the acronym before using it in parenthesis. Then you could just use LHS and RHS for the rest of the paper – N8tron May 23 '18 at 00:46
  • I have never heard this before and would be quite confused and/or bemused to see this in an English language math paper. – Jair Taylor May 23 '18 at 00:47

2 Answers2

3

Better standards are to write

\begin{align}(x-1)^2&=(x-1)(x-1)\tag1 \\&=x^2-x-x+1\tag2\\&=x^2-2x+1\tag3\end{align}

and then refer to the left-hand side (LHS) of $(1)$ or the right-hand side (RHS) of $(3)$.

Regarding the edited question, Google does give some results for "member of the equation". Then again they may be very old, or written by non-native speakers. I've personally never heard it.

Arnaud Mortier
  • 27,276
2

James & James's 1992 Mathematics Dictionary p. 270 gives:

MEM'BER, n. member of an equation. The expression on one (or the other) side of the equality sign. The two members of an equation are distinguished as the left or first and the right or second member.

OED's definition for "member":

7. b. Either of the two sides of an equation.

The quotes it gives for this usage:

1702 J. Raphson Math. Dict. "Equation, (in Algebra) is a Comparison between two Quantities (or Members of the Equation,) to make them equal."

a1831 Encycl. Metrop. (1845) I. 544/2 "Both members of an equation may be raised to the same power, or the same root of them may be extracted."

1859 Ladies' Repository Oct. 626/1 "The equation to be solved is, $x^4−2x^3+x=132$, which, by $\color{green}{\mathrm{transposing*}}$ the second member, may be put under the form, $x^4−2x^3+x-132$."

1903 J. Walker Introd. Physical Chem. (ed. 3) xxvi. 307: "Eliminating what is common to both members of the equation."

1972 M. Kline Math. Thought v. 122: "An expression corresponding to the left or right member reappears under the concept of anharmonic ratio in the work of Pappus and in later work on projective geometry."

So it does appear this is proper (albeit probably rare) modern mathematical English.

$\color{green}{\mathrm{*}}$James & James p. 426:
TRANS-POSE, n., v. To move a term from onemember of an equation to the other and changeits sign. This is equivalent to subtracting the termfrom both members. The equation $x + 2 = 0$ yields $x = - 2$ after transposing the $2$.
OED's "transpose" 5. b.:
Algebra. To transfer (a quantity) from one side of an equation to the other, with change of sign.
Geremia
  • 2,405