Using Formulas with Dates

This should be easy, simple, basic, but I can't figure out why it's not working.

In A1 I have: =TODAY()
In A2 I have: =IF(A1>="1/1/2011",1,0)
A1 returns 1/13/2011, which is correct, todays date.
A2 returns 0. WHY? Clearly A1>1/1/2011 right?


I've worked it a bit and have found that if:

In A2 I have: =IF(A1>=1/1/2011,1,0) (removed the quotations)
A2 returns 1, which is correct.

Keeping A1 the same:
In A2 I have: =IF(A1>=2/1/2011,1,0) (no quotations, greater than February)
A2 returns 0, which is incorrect.
Adding the quotations back in, A2 returns 1, which is correct.

Maybe I'm confused as to when to use quotations and when to not. Without quotations it should just be calculating the value of 1/1/2011, which is a very small number. With the quotations, I thought it should be comparing actual dates.