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In Enderton's 2001 book on mathematical logic, it is stated on page 4 that "every ordered triple is also an ordered pair". More generally, Enderton states that if $=$, it is not necessary that $m=n.$

Could someone point out what definition of equality is used for these statements, and if such a definition is standard? It does not seem to be stated in the said book.

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    You may want to check [this thread](http://math.stackexchange.com/q/2122856/123852). – 2017-02-08
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    it should be $n$ in one of the tuples right? – 2017-02-08
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    @dave yes, sorry for the typo. – 2017-02-08
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    @FabioSomenzi Thanks for the link - I'll take a look. – 2017-02-08

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One of the ways to encode an $n$ tuple $< x_1, x_2, \dots, x_n >$ as a pair $ <, x_n> $. This way as you can represent all finite tuples as a pair. You can get an equality that Enderton describes by having a tuple that matches the representation.