# set theory

#### solakis

##### Active member
Prove in any axiomatic set theory that:

2ε{a,2,b} , where a,b are letters

#### Country Boy

##### Well-known member
MHB Math Helper
What is the definition of "{a, 2, b}" in "axiomatic set theory"? What is the definition of "ε"?

#### solakis

##### Active member
What is the definition of "{a, 2, b}" in "axiomatic set theory"? What is the definition of "ε"?
{a,2,b}={a,2}U{b}

#### topsquark

##### Well-known member
MHB Math Helper
{a,2,b}={a,2}U{b}
Or even better, starting from where you left off: $$\displaystyle \{ a, 2 \} \cup \{ b \} = \left ( \{ a \} \cup \{ 2 \} \right ) \cup \{ b \}$$

-Dan

#### solakis

##### Active member
here is the solution for a similar problem given by seppel in MHF