Tagging - 2017-01-21

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Martin Sleziak

5:51 AM

@JyrkiLahtonen And lo, it is reborn. But I removed it... — pjs36 48 mins ago

straight-lines tag again: math.stackexchange.com/posts/2106376/revisions

Martin Sleziak

6:27 AM

Thanks @pjs36. I would have thought that making it a synonym would have been a permanent cure. Either I did something wrong the first time or... I just don't fully understand these features. — Jyrki Lahtonen ♦ 2 mins ago

So now (straight-lines) is a synonym of geometry.

@JyrkiLahtonen As arjafi epxlains here merging and sysnonymizing are two different things. (And each of them suitable for different situations.) — Martin Sleziak 11 secs ago

@MartinSleziak BTW both those questions about Banach-Tarski paradox are now in HNQ list.

2 hours later…

Martin Sleziak

8:30 AM

specific-question I have added intuition and motivation to Why does the generalised derivative have to be a linear transformation?. The OP explicitly says that they "would like to get an intuitive explanation." And the question is basically about what motivated to define derivative in higher dimensions in certain way.

I have also added multivariable-calculus.

Q: Why does the generalised derivative have to be a linear transformation?

I am starting to learn Real Analysis and I have come across the generalised definition of the derivative for higher dimensions. I realise that the derivative being a linear transformation nicely accommodates the one dimensional case where the derivative is just a constant at any point. I also und...

In any case, I will be glad if somebody revises that tag. (And changes them, if the one I've added are not suitable.)

The question was in HNQ, which caused me to have a look at it.

Martin Sleziak

8:54 AM

specific-question I think that book-recommendation might be suitable here, but that question already has 5 tags: Books on Rings without Identity

Q: Books on Rings without Identity

I was just wondering if anybody knows of any good books or articles that study rings (and algebras) without (or not necessarily with) identity. I have gone through Thomas Hungerford's Algebra textbook (and loved it), but every book I have read afterwards on noncommutative algebra (Farb and Dennis...

abstract-algebra reference-request ring-theory noncommutative-algebra rngs

4 hours later…

Martin Sleziak

1:05 PM

specific-question I have removed algebra-precalculus and added sequences-and-series instead. The tag limits-without-lhopital seems to me a bit out of place, but I was not sure whether to remove it. How do I calculate this limit: $\lim\limits_{n\to\infty}1+\sqrt[2]{2+\sqrt[3]{3+\dotsb+\sqrt[n]n}}$?

Q: How do I calculate this limit: $\lim\limits_{n\to\infty}1+\sqrt[2]{2+\sqrt[3]{3+\dotsb+\sqrt[n]n}}$?

I have seen this question on the internet and was interested to know the answer. Here it is : Calculate $\lim\limits_{n\to\infty}(1+\sqrt[2]{2+\sqrt[3]{3+\dotsb+\sqrt[n]n}})$? Edit : I really tried doing it but wasn't able to get somewhere. I know how to do questions like $ y = (1+\sqrt{1+\...

sequences-and-series limits radicals limits-without-lhopital nested-radicals

1 hour later…

Martin Sleziak

2:08 PM

Newly created tags are tangent-bundle and projection.

For the tangent-bundle the tag creator also created a tag-excerpt.

We already have some tags which are somewhat related such as vector-bundles or fiber-bundles. Somebody who is active in questions from differential geometry might be in a better position to judge whether the newly created tangent-bundle tag might in fact be useful.

Q: Normal bundle and differential of the inclusion map

Let $X$ be a complex manifold and $Y\subseteq X$ a submanifold. I define $TX_{|Y}$ as the restriction bundle of $TX$. How I can prove that $$d \iota: TY\longrightarrow TX_{|Y}$$ ($\iota:Y\longrightarrow X$ is the canonical inclusion) is injective?

algebraic-geometry vector-bundles tangent-bundle

I did no find older discussions about the projection. Using this SEDE query I was able to found a short-lived instance of this tag in 2012.

The tag seems to be non-descriptive in the current state - it has empty tag-info, the word projection can be used in various meanings (linear algebra, equivalence relations, cartesian products). en.wikipedia.org/wiki/Projection_(mathematics)

Q: Suppose $\mathcal{V}$ be a subspaces of $\mathbb{R}^n$,

Suppose $\mathcal{V}$ be a subspaces of $\mathbb{R}^n$, Suppose $P: \mathbb{R}^n\to\mathbb{R}^n$ be a projection, then I need to prove the following $$ \mathcal{V}\cap\text {im } P=P^{-1}\mathcal{V}\cap\text{im }P$$ Suppose $x\in \mathcal{V}\cap\text {im } P\Rightarrow x\in\mathcal{V}\text { a...