# Bidit Acharya

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bio website biditacharya.wordpress.com location Berkeley, CA age 19 member for 3 years, 4 months seen Sep 22 at 8:46 profile views 681

Freshman at UC Berkeley. Originally from Nepal

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. - Henri Poincaré.

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 Aug14 comment Proving that $\mu$ is $\sup S$ Spot on! :) The question says that $\mu$ is the supremum iff there is an element of $S$ in the interval. But what we just did was started out by assuming that there is no element of $S$ in the interval and proved that if this is the case, then $\mu \ne \sup S$. So, for $\mu = \sup S$, there has to be an element of $S$ in the interval Aug14 comment Proving that $\mu$ is $\sup S$ I could elaborate more if you'd like to Aug14 comment Are all infinities equal? I do not mean to do any self-marketing but if you want to learn about this from the beginning, try out this blog post that was recently wrote by me wp.me/p2aEXv-2N . I am writing a follow up article to this and it will be out very soon Aug14 comment Proving that $\mu$ is $\sup S$ $\lambda \not \in S$ means that $\lambda$ is a upper bound for $S$ which is less than $\mu$. If you remember, one of the properties of the least upper bound is that if there exists a quantity that is less than the least upper bound (say $l$), that quantity has to be in the set under consideration. Or else, $l$ can't be the least upper bound Aug14 comment Proving that $\mu$ is $\sup S$ Assume that for some $\epsilon >0$, $\not{\exists} x \in [\mu -\epsilon , \mu]$, such that $x\in S$. This implies that $\exists \lambda < \mu$ where $\lambda \not \in S \implies \mu \ne \sup S$. So if $\mu = \sup S$ then has to be an element of S in the interval $[μ−ϵ,μ]$ Aug14 revised Proving that $2^{2^n} + 5$ is always composite by working modulo $3$ added 326 characters in body Aug14 revised Find all integer solutions to $7595x + 1023y=124$ edited tags Aug14 comment Find all integer solutions to $7595x + 1023y=124$ Are $x,y \in \mathbb Z$? Aug14 comment How to simplify the following basic equation Do you mean, $\text{originalState} + \Big(\frac{\text{animatedState} \big(100 - 100( \text{finishPos} - x )\big) }{ 100(\text{finishPos} - \text{startPos})}\Big)$ Aug14 answered Proving that $2^{2^n} + 5$ is always composite by working modulo $3$ Aug14 comment Help in understanding integration by changing the variable The "ILATE" mnemonic, as @J.M. mentioned is particularly helpful when you are first starting out but then later on, with practice, you will be able to figure out the way without any mnemonics as such. In fact, I think using the mnemonic, while helpful at the beginning, will hinder you intuitive development when it comes to integrating by parts! Aug14 comment Help in understanding integration by changing the variable I believe you are mistaken. The process of integrating by parts is not related to the derivative of a composite function. As André says, it is pretty much a manipulated version of the product rule for differentiation. Aug13 accepted Difference between Dimension of a Linear transformation (space) and the Dimension of its Column Space? Aug13 accepted Show that the dimension of a particular linear space is $2$ Aug8 accepted Proof of a Proposition on Partitions and Equivalence Classes Aug8 comment Trouble relating the two definitions of $(\mathbb Z/n\mathbb Z)^\times$ wow... thank you! I think I got it :) Aug8 accepted Trouble relating the two definitions of $(\mathbb Z/n\mathbb Z)^\times$ Aug8 asked Trouble relating the two definitions of $(\mathbb Z/n\mathbb Z)^\times$ Aug6 revised Combination - How many different ways Basic Tex formatting and revisions in phrasing Aug6 suggested suggested edit on Combination - How many different ways