Equality of n-tuples of different lengths

Question

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 $<x_1, ...,x_m>=<y_1, ...,y_n>$, 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.

You may want to check this thread. – Fabio Somenzi Feb 08 '17 at 00:50 — Fabio Somenzi, Feb 08 '17 at 00:50
it should be $n$ in one of the tuples right? – dave Feb 08 '17 at 00:53 — dave, Feb 08 '17 at 00:53
@dave yes, sorry for the typo. – FreshAir Feb 08 '17 at 00:54 — FreshAir, Feb 08 '17 at 00:54
@FabioSomenzi Thanks for the link - I'll take a look. – FreshAir Feb 08 '17 at 00:55 — FreshAir, Feb 08 '17 at 00:55

score 1 · Accepted Answer · answered Feb 08 '17 at 01:35

One of the ways to encode an $n$ tuple $< x_1, x_2, \dots, x_n >$ as a pair $ <<x_1, x_2, \dots, x_{n-1}>, 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.

Equality of n-tuples of different lengths

1 Answers1