Science Memes

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Science isn't a filing cabinet of facts, it's a conversation. For example, a photo of an eel or other localized wildlife counts because most people never see one, and wonder is the first step of inquiry. A car meme counts if it makes you curious about what's under the bonnet. If you want to talk about something you noticed in the world, chances are someone else wants to talk about it too.

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I just cited myself. (mander.xyz)

submitted 2 years ago by fossilesque@mander.xyz to c/science_memes@mander.xyz

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[–] sp3tr4l@lemmy.zip 1 points 2 years ago (1 children)

https://www2.kenyon.edu/Depts/Math/Paquin/GeomSeriesCalcB.pdf

Here's a standard introduction to the concept of the Convergence/Divergence Theorem of Geometric Series, starts on page 2.

Its quite common for this to be referred to as the convergence test or rule or theorem by teachers and TA's.

[–] Tomorrow_Farewell@hexbear.net 1 points 2 years ago* (last edited 2 years ago)

Now, ask yourself this question, 'is 0.999..., or any real number for that matter, a series?'. The answer to that question is 'no'.

You seem to be extremely confused, and think that the terms 'series' and 'the sum of a series' mean the same thing. They do not. 0.999... is the sum of the series 9/10+9/100+9/1000+..., and not a series itself.

EDIT: Also, the author does abuse the notations somewhat when she says '1+1/2+1/4 = 2' is a geometric series, as the geometric series 1+1/2+1/4+... does not equal 2, because a series is either just a formal sum, a sequence of its terms, or, in German math traditions, a sequence of its partial sums. It is the sum of the series 1+1/2+1/4+... that is equal to 2. The confusion is made worse by the fact that sums of series and the series themselves are often denoted in the same way. However, again, those are different things.
Would you mind providing a snippet with the definition of the term 'series' that she provides?

EDIT 2: Notably, that document has no theorem that is called 'convergence theorem' or 'the convergence theorem'. The only theorem that is present there is the one on convergence and divergence of geometric series.