I Spy a Couple of Crochet Butterflyfish ... Oh, and a Nautilus Too ... 👉 buff.ly/2Yi6U5J #crochet #handmade #art #fiberart

#crochetheart #hearttransplant #crochet

$$ \forall base\geq4 S(base) = 1,11,21,1211,111221,312211,\dots \forall s_i \in S(base), s_i \in \{1,2,3\}* S(3) = 1,11,21,1211,111221,1012211,\dots S(2) = 1,11,101,111011,11110101,100110111011,\dots $$

$$ b\in\mathds{Z}, b>1 D = \{0, \dots, b-1\} \forall x\in\mathds{Z} x = d_0 + d_1b + \dots + d_nb^n x = 0 \mod (b-1) \Leftrightarrow \sum_{i=0}^n (d_i) = 0 \mod (b-1) $$

$$ a,b\in\mathds{R^+}, a\neq b wlog, a < b \frac{b}{b-a} - \frac{a}{b-a} = 1 \exists d\in\mathds{N} : d\in\[\frac{a}{d}, \frac{b}{d}\) da+1 \leq db \exists n\in\mathds{N} : n-1 \leq da < n da < n < da+1 \leq db a < \frac{n}{d} < b $$

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$\text{Party time.}$

$$ G:= (V,E): \forall e\in E, e := (a,b) P:= \{p \in E*: \forall e_i \in p, b_i=a_{i+1}\} X:= |E| = |V|-1 Y:= \forall p \in P, a_0 \neq b_{|p|} Z:= \forall a,b \in V, \exists p \in P: a=a_0 \wedge b=b_{|p|} X \wedge Y \Leftrightarrow Y \wedge Z \Leftrightarrow X \wedge Z $$

$$ x:=\product_{p\in P}(p) |P|\in\mathds{Z} \Rightarrow \exists p_0\in P : (x+1)\mod p_0 = 0 \Rightarrow \exists n\in\mathds{N} : np_0 = 1+x = 1+\frac{x}{p_0}p_0 \Rightarrow p_0(n-\frac{x}{p_0}) = 1 \Rightarrow p_0 = 1 \wedge (n-\frac{x}{p_0}) = 1 1\notin P \wedge p_0 \in P $$

$$ s_n = \sum_{i=0}^n(\frac{1}{r})^i rs_n = r + s_{n-1} = r + s_n - r^n (r-1)s_n = r - r^n s_n = \frac{r}{r-1} - \frac{r^n}{r-1} r > 1 \Rightarrow s_\infty = \frac{r}{r-1} $$

QUINARY ANNOUNCEMENT: We watched the roster changes with interest, and now we have a new signing of our own to announce. We hope our fans will join us in giving a warm Spies welcome to the one and only Vriska Serket.

$$ x^2 + 2bx = c (x+b)^2 = x^2 + 2bx + b^2 = c + b^2 x + b = \sqrt{c+b^2} x = \sqrt{c+b^2} - b $$

$$ \exists c \in\mathds{Q} : c^2 = 2 \Rightarrow \exists a,b\in\mathds{Z} : c=\frac{a}{b} \wedge \gcd(a,b) = 1 \wedge (\frac{a}{b})^2 = 2 \Rightarrow a^2 = 2b^2 \Rightarrow \exists n\in\mathds{N} : a = 2n \Rightarrow a^2 = (2n^2) = 4n^2 = 2b^2 \Rightarrow gcd(a,b) \geq 2 $$

I Am Once Again Being Haunted By The One Known As Hatsune Miki They Are Telling Me To Make Hamburgers With The Pickles Inside The Hamburger I Will Complete This Abominable Culinary Appeasment

Hi, everybody! Sorry that I've been a bit behind on the twitter — happy to be back & talking with all y'all :-) 🌟

I'm ironing my jersey. Excited to get back into the game tomorrow — I feel like we have a real shot at winning this season! Just need to make it through some minor reverb. :-) 🌟

Fun Math Fact Of The Day: the principle of explosion says that if you start from a contradiction, you can get anything you want. But you can't get them back. :-) 🌟