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α

Kimi Pārōnaki e ai ki α

1

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Aromātai

α

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Pātaitai

α

Ngā Raru Ōrite mai i te Rapu Tukutuku

The set of ordinals

< α

of a given cofinality

κ < cf (α)

https://math.stackexchange.com/questions/1294143/the-set-of-ordinals-alpha-of-a-given-cofinality-kappa-textcf-alpha

g

is a strictly increasing continuous function, and

κ

is regular. So this is reduced to showing that

g (κ)

κ

. One direction is trivial, it is certainly ...

α \in N^{n}

α!

https://math.stackexchange.com/questions/1943545/if-alpha-in-mathbbnn-then-what-is-alpha/1943548

It's simply the product of all the factorials: Suppose you have

α = (α_{1}, . . ., α_{n}) \in N^{n}

α! = α_{1}! \cdot . . . \cdot α_{n}!

D_{8}

as a semidirect product

V ⋊ C_{2}

https://math.stackexchange.com/q/242202

If you know a bit more about group theory you could always do the following: There is a non-trivial semi-direct product of

V

C_{2}

A u t (V)

contains an element of order

2

Proof that Radius of Convergence of Power Series is

1

https://math.stackexchange.com/questions/2388544/proof-that-radius-of-convergence-of-power-series-is-1

Your proof is almost valid, but unfortunately The sequence is bounded so,

l i m s u p ∣ a_{n} ∣^{1 / n} = 1 .

= α

is wrong for several reasons. First, it wasn't clear what

α

is; I had to ...

{x \in R_{+}^{n} : w \cdot x \leq α}

w, α \in R_{+ +}^{n}

https://math.stackexchange.com/questions/2020549/showing-that-x-in-mathbbrn-w-cdot-x-le-alpha-for-w-alpha-in-m

HINT: the function

f : R_{\geq 0}^{n} \to R, x \mapsto w \cdot x = \sum_{k = 1}^{n} w_{k} x_{k}

w_{k} \in R_{> 0}, \forall k

is continuous. If you show that the set

[0, α]

R

\sum x^{n} (1 - \frac{2 x}{π})^{n} tan^{n} x

converges uniformly.

https://math.stackexchange.com/q/1007704

f (x) = x (1 - \frac{2 x}{π}) tan x

is nonnegative and increasing in

[0, α]

f (α) < 1

α < π / 2) .

∣ ∣ ∣ x^{n} (1 - \frac{2 x}{π})^{n} tan^{n} x ∣ ∣ ∣ = ∣ ∣ ∣ x (1 - \frac{2 x}{π}) tan x ∣ ∣ ∣^{n} \leq (f (α))^{n} .

Tohaina

Kua tāruatia ki te papatopenga

\alpha ^{1-1}

Ko te pārōnaki o ax^{n} ko nax^{n-1}.

\alpha ^{0}

Tango 1 mai i 1.

1

Mō tētahi kupu t mahue te 0, t^{0}=1.

Ngā Tauira

whārite tapawhā

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whārite paerangi

y = 3 x + 4

699 * 533

[2534] [2 - 1 0135]

whārite Simultaneous

{8 x + 2 y = 46 7 x + 3 y = 47

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