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Unformatted text preview: anteed to be at least 1. In other words, there is no real solution to
this equation. For the same basic reason there is no solution to the inequality. Squaring any real
x makes it positive or zero and so will never be negative.
We need a way to denote the fact that there are no solutions here. In solution set notation we say
that the solution set is empty and denote it with the symbol : Æ . This symbol is often called the
We now need to make a couple of final comments before leaving this section.
In the above discussion of empty sets we assumed that were only looking for real solutions.
While that is what we will be doing for inequalities, we won’t be restricting ourselves to real
solutions with equations. Once we get around to solving quadratic equations (which x 2 + 1 = 0
is) we will allow solutions to be complex numbers and in the case looked at above there are
complex solutions to x 2 + 1 = 0 . If you don’t know how to find these at this point that is fine we
will be covering that material in a couple of sections. At this point just accept that x 2 + 1 = 0
does have complex solutions.
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12