“Irrational numbers are those real numbers which are not rational numbers!” Def.1: Rational Number A rational number is a real number which can be expressed in the form of where $ a$ and $ b$ are both integers relatively prime to each other and $ b$ being non-zero.Following two statements are equivalent to the definition…
If you are aware of elementary facts of geometry, then you might know that the area of a disk with radius $ R$ is $ \pi R^2$ . The same is true for a geometric circle. The difference between a disk and a circle lies in dimensions, as the disk is a two-dimensional object and…
Weierstrass introduced the idea that there exist functions that are continuous for every value of $x$ but do not possess a derivative at any value of $x$. We now consider the celebrated Weierstrass function, which exhibits this property. In this note, I will demonstrate that such a function exists using Weierstrass’s construction. The Weierstrass Function…
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