Qualifier’s order

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The order is important!

(a) & (b) have different meanings:

(a): For all M in R, there exists n in N such that

(b): There exists n in N such that for all M in R, …

See also example below:
https://tomcircle.wordpress.com/2013/05/30/sequence-limit/

Ref: “The Math Girls
http://www.amazon.com/gp/aw/d/0983951349/ref=pd_aw_cart_recs_1?pi=SL500_SY115

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