A relation R on set A is reflexive if for every x in A, x R x. This can be written in mathematical form as follows.


This is read as "for all x in (set) A, (condition) x R x (is true)"

Universal quantification involves "for all" within a certain domain set.

• The symbol "∀" is read as "for all".
• The symbol "∈" is read as "in" which is short for "is an element of" (the domain set that follows).
• The symbol ":" (colon) can be thought of as saying "such that" or "it is true that" (what follows).

The "there exists" symbol "∃", and many others, were created by the Italian mathematician Giuseppe Peano (1858-1932), many by reversing letters or turning them upside down.

Peano created the "or" symbol as "∨" from the letter "v" starting the Latin word "vel" ≈ "or". The "and" symbol "∧" is an upside down "or" symbol.

Other mathematicians then followed this convention in creating more symbols over time. One such symbol was the "for all" symbol "∀" first used in 1935 by logician Gerhard Gentzen (1909-1945) and called it, in German, "All-Zeichen", the "all character"

An example is as follows.


This is read as "for all x in the set 1, 3, 5, x is an add number"

Rather than specify what one has done, management may generalize what you have done as "Thank you for all that you do".

Translation: It is too hard to actually determine what you did or list everything that you did. It is much less for us to make a vague general statement that covers everything that you might have done.

Here is the math for "Thank you for all that you do".


The word "thank" is related to the word "think".

• The German word "denken" ≈ "think".
• The German word "danken" ≈ "thank".

Here is the diagram to summarize these laughing ideas.