The order is important!
(a) & (b) have different meanings:
(a): For all M in R, there exists n in Nsuch that …
(b): There exists n in Nsuch that for all M in R, …
See also example below:
http://tomcircle.wordpress.com/2013/05/30/sequence-limit/
Ref: “The Math Girls”
Mathtuition88 