SOLUTION: explain how interval notation set notation and inequality notation are all related
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Question 1178099: explain how interval notation set notation and inequality notation are all related
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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https://saylordotorg.github.io/text_elementary-algebra/s05-07-introduction-to-inequalities-a.html#:~:text=Two%20common%20ways%20of%20expressing,them%20on%20a%20number%20line&text=and%20indicates%20that%20the%20set,is%20included%20in%20the%20solution.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Is interval notation the same as set notation?
It's just a different notation to express the same thing. On the other hand, if you want to represent the set with interval notation, you need to know the upper and lower bound of the set,
Set-builder notation is a list of all of the elements in a set, separated by commas, and surrounded by French curly braces. The symbol " | " is read as "such that". It may also appear as " : ", meaning "such that".
Interval notation is a clean and easy way of expressing an interval as an inequality.
for example: "All the real number x(x∈R) such that (the symbol "|") xis between 2and 10=>(2
or possibly the upper and lower bound of all the intervals that compose the set.
for example: if your set is composed by all the numbers smaller than 5, or between 10 and 20, or greater than 100, you write the following union of intervals:
(−∞,5) ∪ (10,20) ∪(100,∞)
Two common ways of expressing solutions to an inequality are by graphing them on a number line, and indicates that the set is unbounded to the right on a number line.
Interval notation requires a parenthesis to enclose infinity. The square bracket indicates the boundary is included in the solution.
All Three Methods Together
Here is a handy table showing all 3 methods (the interval is 1 to 2):
................................From 1 ................................ ............................ To 2
................................Including 1.............. Not Including 1..............Not Including 2.............. Including 2
Inequality:.............. x ≥ 1.....................................x > 1..................................x < 2...................x ≤ 2
.........................."greater than or equal to".........."greater than"......."less than"...."less than
or equal to"
Number line: ...............≥1............... >1.............................. <2............... ≤2
Interval notation:............... [1............... (1.............................. 2)............... 2]
Example: to include 1, and not include 2:
Inequality: x ≥ 1 and x < 2 or together: 1 ≤ x < 2
Number line: ≥1<2
Interval notation: [1, 2)
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