/sci/ - Science & Math

c<rad(abc)^1.001

With only finitely many counter-examples

Based Jenssen's inequality

|x-y| <= |x-z| + |z-y|

Quite useful in analysis, it helped me a lot.

call me a basic bitch if you want but cauchy schwarz delivers every time

>>9909361
You only took the log of the AM-GM inequality.

I have a whole book about inequalities.
I don't know, Minkowski and Hoelder are pretty cool.

I thought this was really neat when my prof first wrote it on the board.

Let [math]\left(D,\;\mu\right)[/math] be a measured space and [math]\left(\mathbf V,\; +\; \cdot,\; \left\|\cdot\right\|\right)[/math] be a normed vector space.
[eqn]\color{green}{\tt Minkowsi's\;inequality:}\qquad \forall p \;\in\; \overline{\left[1,\; \infty\right)},\; \forall\left(f,\,g\right) \;\in\; L^p\left(D,\,\mathbf V\right),\; \left\|f\,+\,g\right\|_p \;\leqslant\; \left\|f\right\|_p \,+\, \left\|g\right\|_p[/eqn]

>>9909495
>>>/pol/

← Dorin Andrica's Conjecture

>>9909588
What the hell is the meaning of that closure line? You meant to include infinity? Why not just use inclusion bracket?

>>9909752
Because [math]\left[1,\; \infty\right][/math] would imply [math]\infty[/math] is a number.

>>9909764
Well, the closure of that set is the set itself in the topology induced by the Lebesgue measure, so the notation is meaningless. At least the inclusion would be intuitive and you're effectively treating infinity as a number anyway.

>>9909782
>the topology induced by the Lebesgue measure
Pretty sure that doesn't exist, or at least isn't standard.