Sophism #10: Continued FractionssteemCreated with Sketch.

in #math7 years ago (edited)

Number one may be represented as an infinite continued fraction as follows:

formula.png

Number two may also be represented in exactly the same way:

formula.png

Consequently, we should conclude that 1 = 2.


Please, avoid posting spoilers in the comments. For other sophisms check out this list.

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When it comes to analysis, the devil is in the ellipses...

True.

(I do have a geometry/calculus sophism about actual ellipses (the shapes) as well, by the way, so stay tuned for the devil in these ones as well ;)

Hi, these sophism are amusing, but I don't understand why you don't want people to comment. The fun is in unpicking the logic and the false step. Posts only get rewarded for 7 days - you can repost them in a few months and get a largely fresh audience.
Just my thoughts.

and for newbies...

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Well, I don't exactly want to have a big fat spoiler lying right under every puzzle or sophism, because in my opinion it destroys the whole pleasure of the Aha! moment one has the chance to get when they solve it on their own.

Consequently, to reduce the risk of seeing the solution before one gets a time to think about it, I would prefer to have the spoilers detached in time and space from where the puzzle is posted (for example, a separate discussion post may make sense). Indirect hints or related keywords are fine, in my opinion, for example.

Another possible option would perhaps be having a dedicated <spoiler> tag for posting spoiler comments, and I hope it would get implemented eventually as well.

I do understand that reposting would bring new audience, but this mechamism seems stupid and flawed to me, so here as well I hope that the system itself will change to the better before I might have to resort to stupidity.

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