# Correct phrase for “Chain of equations”

In math, one often writes

a = b = c = d

to prove that a=d. How is such a sequence of equations called in English?

In German, there is “Gleichungskette”, but the direct translation “Chain of equation” is not found very often by Google, hence my query.

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"Chain of equation" would be confusing. It made me first think of a series of equations leading to a result. – gmcgath May 23 '13 at 13:58

## 2 Answers

continued equality (mathematics)

An expression in which three or more quantities are set equal by means of two or more equality signs.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

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Strange that I have never heard of it. But thanks! – Joachim Breitner May 23 '13 at 13:57
xdict.net/en/continued%20equality translates it as "Fortsetzung Gleichstellung." – rajah9 May 23 '13 at 14:19
@JoachimBreitner: You're welcome. I've never heard of it either, but it's actually in the cited dictionary :) – Stan May 23 '13 at 14:26
@rajah9: I know nothing about German, but it seems xdict.net has just done a word-for-word translation for the terminology. – Stan May 23 '13 at 14:32
-1: I don't think this is the usual term; I think that would be "chain of equalities". Look at this Ngram. "Chain of equalities" is slightly more frequent than "continued equality". But if you look at the actual examples, 80% of the instances of "continued equality" have nothing to do with mathematics, while most of the ones for "chain of equalities" do. – Peter Shor Feb 17 '14 at 22:57

This is called the Transitive Property of Equality. The page uses your example (without the d).

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Joachim is not asking about the name of the property that his sequence demonstrates (ie. that a=d because of the chain of equations); rather, he is asking about the name for the sequence of equations itself (`a=b=c=d`). – Mark Bannister May 23 '13 at 13:22