For All Notation

For AllNotation

The (for all) symbol is used in math to describe the meaning of one or more variables in a statement. Typically, the symbol is used in an expression like this:

In plain language, this fragment expression means for all in the set of real numbers. Then, this expression is usually followed by another statement that should be able to be proven true or false.


For example, the expressions below describe the meaning of the two variables and and then proposes a statement that is either true or false.

This is read as “for every and belonging to the set of real numbers”.

This second statement represents the square of the sum of two numbers[1] and represents the author’s claim. This statement either holds true for every possible combination of two numbers belonging to the set or it doesn’t.

As a consequence of the for all notation – if you are able to find any combination of two numbers in the set of real numbers where the equality statement is false, then the whole claim is false.


  1. Calculate A Plus B Squared
    Wumbo (internal)