There is an alternative and equivalent statement of the 1/3-2/3 conjecture in the language of probability theory.

The theorem can also be obtained by proving numerous equivalent statements, some of which are summarized below.

An equivalent statement is that for any real number, there are integers both larger and smaller.

An adult who makes an equivalent statement, however, might find his own nose swollen and hurting within seconds.

In this case, the above definition can be characterized by the following equivalent statement:

Contains a brief introduction to the "calculus of equivalent statements."

There are many other equivalent statements of the axiom of choice.

It takes the form of an equivalent statement, to the effect that a certain generalized function is positive definite.

Any of the following equivalent statements is referred to as the Bass conjecture.

Then one may make several equivalent statements about such a set.