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Inequality Chained Notation

Tool to give upper and lower bound of a number (inequality chained notation), search for upper and lower inequalities of a number..

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Inequality Chained Notation -

Tag(s) : Mathematics, Notation System

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# Inequality Chained Notation

## Inequalities Solver

### What are the upper and lower bounds of a number? (Definition)

The notation inequality chained (brackets) $a < b < c$ describes a double inequality $a < b$ and $b < c$ by a lower bound ($a$) and a upper bound ($c$) of the number $b$.

### 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 finds 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: $x \in ]1,2] \iff 1 < x \leq 2$

### How to find a number between 2 other numbers?

Given 2 distinct numbers $n_1$ and $n_2$ with $n_1 < n_2$, then there is always an infinity of numbers between the 2, in particular the mean of the 2 numbers: $n = (n_1 + n_2)/2$ which is such that $n_1 < n < n_2$

Example: $n_1 = 1/5$ and $n_2 = 1/4$ then the mean $n = (1/5+1/4)/2 = 9/40$ is such that $n_1 < n < n_2$

## Source code

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Inequality Chained Notation on dCode.fr [online website], retrieved on 2024-06-25, https://www.dcode.fr/chained-inequality

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