Irrational Numbers: Examples & Non-Examples Explained

High School
Algebra
Algebra I
Irrational numbers

Are certain measurements always irrational numbers?

fabler107 2022-11-18

Statements about addition, multiplication and exponentation with rational and irrational numbers
For every rational number $x$ and every irrational number $x + y$ is irrational.

Celeste Barajas 2022-11-18

Does exist a function $f$ that discontinuous at rational and continuous at every irrational but the restriction $f$ to the set of all irrational numbers is not constant and $f (q_{n})$ is convergent where ${q_{n}}$ is a sequence of rationals.
Thomae function is one of an example of function that satisfies above condition if the restriction $f$ to the set of all irrational numbers is constant.

Rigoberto Drake 2022-11-17

How to know that irrational numbers never repeat?

vedentst9i 2022-11-17

Are there any irrational numbers that have a difference of a rational number?

Siena Erickson 2022-11-17

Let $τ$ be a topology on a set $X$ and consider $A \subseteq X$ . If $x \in X$ is an accumulation point of $A$ if:
$\forall U \in τ, x \in U ⟹ A \cap U$ contains another point other than $x$ .

tramolatzqvg 2022-11-17

If now we have two irrational numbers $α$ and $β$ , can we find sequences ${a_{n}}$ , ${b_{n}}$ and ${q_{n}}$ with $q_{n} \to \infty$ as $n \to \infty$ such that
$| α - \frac{a_{n}}{q_{n}} | < \frac{1}{q_{n}^{2}} and | β - \frac{b_{n}}{q_{n}} | < \frac{1}{q_{n}^{2}} ?$

Josie Kennedy 2022-11-17

Show that $| I | = | R |$

piopiopioirp 2022-11-16

If $a, b, m$ and $n$ are positive integers such that $\sqrt[m]{a}$ and $\sqrt[n]{b}$ are irrational numbers, how can we prove that the sum $\sqrt[m]{a} + \sqrt[n]{b}$ is also irrational?

fabler107 2022-11-16

Are there many more irrational numbers than rational?

Emma Hobbs 2022-11-15

Is " $120 %$ " an integer or irrational number ?

Siemensueqw 2022-11-15

Show that $0.1248163264...$ is irrational

drzwiczkih5a 2022-11-14

Let $X = R$ and $S$ be the set of irrational numbers. Find the closure of $S$ in the following topologies for $R$
The topology of the accounting complement

piopiopioirp 2022-11-14

Let $q$ be irrational. Let $a, b$ be rationals such that $a < q < b$ . If there exists an element $p$ s.t. $a < p < b$ , would it be valid to conclude $q = p$ ?

vidamuhae 2022-11-14

Are all irrational algebraic numbers normal?

Annie French 2022-11-14

Why is a base $10$ decimal "fraction" okay but a non base $10$ fraction not okay?

Annie French 2022-11-13

Find an example where the expression is rational, or give a proof of how it has to be irrational?

spasiocuo43 2022-11-13

Prove or disprove that the sum of two irrational numbers is irrational

Ayanna Goodman 2022-11-12

Why must we distinguish between rational and irrational numbers?

Hayley Mcclain 2022-11-12

False or true, with $m$ and $\in$ ?
If $m$ is a rational no negative number and $n$ an irrational number, then $m n$ is irrational.

The use of irrational numbers is quite common for the Engineering disciplines where various irrational numbers equations are used to determine the rightfulness of some calculations or tasks that require prognosis. As a way to make things easier, you can take a look at the list of questions related to irrational numbers and receive immediate help as you look through the list of answers.

If you need additional assistance or feel unsure about your task, simply compare these examples with your task and proceed from there.

Algebra I

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