# What is the simplest mathematical object? [closed]

What is the simplest mathematical object? I am talking about mathematics in the most abstract way possible, and not as some concrete axiomatic theory (e.g. foundational ones, like ZFC).

After a lot of time pondering this question I came to the opinion that the answer is the equality relation.

P.S. This question is a tiny bit opinion-based, so I decided to post it under the philosophy and soft-question tags.

## closed as off-topic by John B, Dietrich Burde, Alex M., Andrés E. Caicedo, J.-E. PinMar 16 '16 at 14:09

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• What exactly is a mathematical object ? – Dietrich Burde Mar 16 '16 at 12:38
• Perhaps not a "mathematical object," but I'd think the $=$ sign is fairly simple. (Not that people don't misuse it, sometimes incorrectly writing things like $5\times2=10+3=13$.) – Akiva Weinberger Mar 16 '16 at 12:40
• What could be simpler than the empty set? – Gerry Myerson Mar 16 '16 at 12:43
• @GerryMyerson $0$ is "simpler" than $\emptyset$ (for writing). – Dietrich Burde Mar 16 '16 at 12:47
• A psychologically simple object might not be a logically simple one. $0$ is logically very simple, yet the Romans did not have it in their number system; the Arabs had to import it from the Indians, who were well versed into thinking about "nothingness". On the contrary, the natural numbers (starting with $1$) are psychologically very simple (even kids can understand them), but constructing them rigorously is not trivial (think of Peano). As you see, simplicity is not that simple. – Alex M. Mar 16 '16 at 12:47

• I find the idea of the number $1$ simpler than my index finger – vrugtehagel Mar 16 '16 at 12:48
• @vrugtehagel: That's because you live in 2016 A.D., having acquired a mathematical education and a view on the development of mathematics. Had you lived in 2016 B.C., you wouldn't have even understood what the words "the idea of the number $1$" mean. – Alex M. Mar 16 '16 at 12:51