In your hypothetical, if you claim at 64 you would get $1,000/month the first year and $1,030 the second year. If you claim at 65 you would get $1,133/month the first year (the year you would get $1,030 if you claimed at 64). So you get an increase because you claim later and that increase is adjusted for COLA increases.
If something cannot endure laughter.... it cannot endure.
Patience is the art of concealing your impatience.
Slow and steady wins the race.
Retired Jan 2012 at age 56...target
65/35/0 AA TBD