Tool to give upper and lower bound of a number. The inequality chained notation a < b < c stands for a < b and b < c which describes a double inequality with a lower and upper bound of the number b.
Inequality Chained Notation - dCode
Tag(s) : Mathematics, Notation System
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Inequality Chained Notation
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Upper and Lower bound of a Number
Tool to give upper and lower bound of a number. The inequality chained notation a < b < c stands for a < b and b < c which describes a double inequality with a lower and upper bound of the number b.
Answers to Questions
How to find upper and lower bounds of a number?
To find upper and lower bounds of a number, make rounding according to a given precision or multiple and return a result with the inequality chained notation.
Example: \( 1.23 \) rounded to one digit after decimal point to upper bound is \( 1.2 \), and \( 1.3 \) to lower bound. The representation with a double inequality is $$ 1.2 < 1.23 < 1.3 $$
dCode find the upper bound and the lower bound of the number according to the required accuracy. Inequality is strict by default, but can sometimes introduce less than or equal signs.
Inequalities display the boundaries in order from the smallest to the biggest limit. But it is possible to write them in reverse $$ 1.3 > 1.23 > 1.2 $$
How to write a definition domain into a chaine inequality?
A domain of definition of a function is equivalent to an equality:
Example: \( x \in [0,1[ \iff 0 \leq x < 1 \)
Example: \( x \in ]1,2] \iff 1 < x \leq 2 \)
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Source code
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