I'm reading though my analysis book and a came across this it says the following is true
(∀n∈N)(∃m∈N) m>n
which i understand but the follow is not:
(∃m∈N)(∀n∈N) m>n
which i dont get at all they both seem true to me. Could someone explain please
I'm reading though my analysis book and a came across this it says the following is true
(∀n∈N)(∃m∈N) m>n
which i understand but the follow is not:
(∃m∈N)(∀n∈N) m>n
which i dont get at all they both seem true to me. Could someone explain please
Just read them aloud. The first says, "for any n, there exists an m such that m>n", i.e. for every number there's a bigger number, clearly true.
The second says, "There exists an m, such that for any n, m>n", i.e. there's a number that's bigger than every other number, clearly false.