Hello everyone! this is my first note in the Inequalities series. I'll be posting many notes and whacky questions in this series, so stay tuned and enjoy mathematics. PS : These notes will be of REAL help for IIT preparation as well.
Set of numbers between any two real numbers ( ) is called an interval.
For example: Consider a variable whose possible values lies strictly between and , including . Thus, we can say that:
[ NOTE1: Since , we write and not ]
Alternatively, this can be represented in interval form as:
In general, for
This interval form can be represented on the number line as follows :
[ NOTE2: We never use a closed interval for . In other words, we never equate the variable to infinity. For example: Set of all real numbers can be expressed as ]
1. If the roots of the following equation belong to the set . Find the maximum possible integral value of a.
2. Find the number of integers ( ) satisfying
3. Frame your own interesting question and post it down below in the comments.
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Stay tuned for more notes and questions. You can even post your matter down here in the comments to make this topic more interesting. (I've reserved the advanced topics and properties for upcoming notes.)
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Complete set here : Inequalities
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