# Math Help - Prueba

1. ## Prueba

How can I demostrate that language $\Gamma$ have words of any large exept two?

$(i) \epsilon\in\Gamma$
$(ii)a\in\Gamma$
$(iii)\mbox{ If } \alpha\in\Gamma\mbox{ and }\beta\in\Gamma, \Rightarrow b\alpha c\beta b \in\Gamma$

Thank you!

2. I got a mistake in the title but don't know how to change it

3. How can I demostrate that language have words of any large exept two?
Of any length? The set $L$ of lengths of words in $\Gamma$ has the following properties: $0\in L$; $1\in L$; $m,n\in L\Rightarrow m+n+3\in L$.

Show that $3,4,5\in L$. Then 0+3+3=6, 0+4+3=7 and 0+5+3=8 are also in $L$. This can be continued.

4. Thanks emakarov!

Yes of any length, I can proof by induction method on the basis of the induction definition you gave...