It is seems to be an easy question, I wonder why googling didn't give anything helpful -- nor in StackOverflow, nor in tutorials. I just need to check using bash that a condition is false.
Of what I found I tried
if ! [ 0==2 ]; then echo Hello; fi
if [ ! 0==2 ]; then echo Hello; fi
Do you mean:
if ! [ 0 == 2 ]; then echo Hello; fi
You lacked space around the equality operator.
This might be the time to read http://tldp.org/HOWTO/Bash-Prog-Intro-HOWTO.html - especially the sections about if then else and operators. I usually have this open when I am writing scripts..