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.

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