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Who is the mathematician who proved that empty set is subset of all sets and made it known to most mathematicians? I looked into the ripple effects in the mathematical world that would occur if the vacuous truth were false, and the most articles were about the empty set. So, in order to learn more about this, I wanted to investigate a mathematician who made it clear to the mathematical community that empty set is subset of all sets.

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Giuseppe Peano, Studi di Logica matematica (1897):

Il segno $\Lambda$, fra classi, indica la classe nulla, cioè non contenente alcun individuo. Si può definire come segue [The $\Lambda$ symbols denotes the null class. It is defined as follows (original symbols slightly modernised)]:

$a \in \text {Class} \to [(b)[b \in \text {Class} \to (a= \Lambda \equiv a \subset b)].$

"Sia $a$ una classe; diremo che la classe $a$ è nulla se, comunque si prenda la classe $b$, la $a$ è contenuta in $b$. [Let $a$ a class; we will say that $a$ is a null class when, whatever class $b$ is, $a$ is included into $b$]".

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    $\begingroup$ I have been receiving help for a few days now. Thank you very much for your answer. $\endgroup$ Commented Apr 15 at 9:40
  • $\begingroup$ @user1274233 - you are welcome :-) $\endgroup$ Commented Apr 15 at 10:04

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