cravetheintangible

I am Danielle. 20. Currently a student at UTPA (Southern Texas!). Physics major. Astronomy minor. I love the cosmos & most science related things! Have questions/comments? Ask away :D

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Proof: Polynomials as Sequences

One reason polynomials are interesting is that you can use them to encode sequences.

$\begin{matrix} 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + \cdots \\ \\ 5 + 2 \, x + 13 \, x^2 + 87.1 \, x^3 - x^4 + x^5 - 3 x^6 \cdots \\ \\ (\ 5, \ \ 2, \ \ 13, \ \; 87.1, \ -1, \ \ 1, \ -3, \ \ldots\ ) \\ \\ a + b \, x + c \, x^2 + d \, x^3 + e \, x^4 + f \, x^5 + g \, x^6 + \cdots \\ \\ \sum_0^N \mathrm{const}_i \cdot x^i \end{matrix}$

In fact some of the theory of abstract algebra (the theory of rings) deals specifically with how your perspective changes when you erase all of the x^297 and x^16 terms and think…

(Source: isomorphismes)

77 notes ! Reblog ! 3 months ago

Posted on January 28th at 4:09 PM
Reblogged from: proofmathisbeautiful
Originally posted by: isomorphismes

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FUCK YEAH HOLY FUCK I LOVE THIS STUFF LET ME IN THIS GODDAMN CLASS I DON’T WANT TO MISS OUT
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probably aren’t...my followers, but insanely interesting
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My guess is that one day we discover that everything is 0.
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