What's wrong with writing the state "x<2 or x>5" as 5<x<2?

What's wrong with writing the state "x<2 or x>5" as 5<x<2

2 Answers
Daniel L.
Sep 13, 2017

See explanation.

Explanation:

Those statements describe different sets of numbers:

First one describes numbers which are either less than #2# or greater than #5#. In other words it describes interval:

#x in (-oo;2) uu (5;+oo)#

The second statement describes numbers which are greater than #5# and less than #2#, but there are no such numbers. If a number is greater than #5# it is also greater than #2#.
So the second statement describes an empty set.

Alan P.
Sep 13, 2017

#5 < x < 2# implies that #x# must be both #> 5# and # < 2#

Explanation:

There are no values of #x# which satisfy # 5 < x < 2#

For example, if #x=6# so that #5 < x#
then #x cancel(<) 2#

#x < 2# or # x >5# has many solutions
since only one of the conditions needs to be met for the qualification to be true.

Related questions
Impact of this question
1043 views around the world
You can reuse this answer
Creative Commons License