1

enter image description here

Why is the \exists k used in this set-builder notation?

waterlemon
  • 189
  • 1
    "The set of all integers $n$ such that there exists an integer $k$ allowing us to write $n = 2k$." – Kaj Hansen Nov 10 '16 at 08:59
  • it is part of the definition of the set, set like ${n\in \Bbb Z| (\forall k\in \Bbb Z)[n=2k]}$ also make senses(though I defined an empty set) – Nick Nov 10 '16 at 08:59

1 Answers1

2

It always helps to read the mathematical notation with full sentences:

The set of all such integers $n$ for which there exists some integer $k$ such that $n$ is equal to $2\cdot k$.

So, the "there exists" is vital in the definition of the set.

5xum
  • 123,496
  • 6
  • 128
  • 204