This is beta site. https://beta.mathcity.org/ 2026-06-05T09:21:00+00:00 https://beta.mathcity.org/ https://beta.mathcity.org/_media/logo.png text/html 2025-01-21T16:13:55+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/dyk/1?rev=1737476035&do=diff Are the functions are same? [Are the functions are same?] Consider two functions $f(x)=x+3$ and $\displaystyle g(x)=\frac{x^2-9}{x-3}$. Is $f=g$? Answer <WRAP center round red 70%> A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. </WRAP>$f:A \to B$$f = A$$B$$A$$A$$B$$A=\mathbb{N}$$B=\mathbb{R}$$f(x)=x+1$$1 \mapsto 2$$\quad 2 \mapsto 3$$\quad 3 \mapsto 4$$f = \mathbb{N}$$A=\mathbb{R}$$B=\mathb… text/html 2025-01-21T16:13:55+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/dyk/2?rev=1737476035&do=diff What is the value of pi? <div><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Pi-unrolled-720.gif/220px-Pi-unrolled-720.gif" title="Did you know?" class="mediaright" alt="What is pi??" /></div> What is the value of $\pi$? * (A) 3.1415 * (B) $\frac{22}{7}$ * (C) $\frac{333}{160}$ * (D) None of these ✔ Answer <WRAP center round red 70%> The number π is a mathematical constant, the ratio of a circle's circumference to its diameter. It is an irrational number, meanin… text/html 2025-01-21T16:13:55+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/dyk/3?rev=1737476035&do=diff Its about square root [DYK] The reason is not difficult if one knows about the definition of square root of real numbers. Definition: Let $x$ be a non-negative number. Then a non-negative number $r$ is called square root of $x$ iff $r^2=x$. Square root of $x$ is denoted by $\sqrt{x}$$2^2=4$$3^2=9$$x$$r$$x$$r^2=x$$2^2=4$$(-2)^2=4$$\sqrt{4}=\sqrt{2^2}=\sqrt{(-2)^2}=2$$\sqrt{4}=\sqrt{2^2}=\sqrt{(-2)^2}=\pm 2$$\sqrt{4}$$\sqrt{x}$$x\geq0$$\sqrt{x}=x^{\frac{1}{2}}$ text/html 2025-01-21T16:13:55+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/dyk/4?rev=1737476035&do=diff Is it difficult to answer? 1−−−0.999… [Is 1=0.999...?] This is a simple and common question asked to students, who have passed higher secondary school certificate. Most of the student unable to give the correct answer. Well, we cannot predict the exact reason but one simple reason seems to be a lack of logical reasoning. For example, if we wish to round off $0.999...$$x=0.999...$$10x=9.99...$$10x=9+0.999...$$10x=9+x$$9x=9$$x=1$