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Showing posts from December, 2019

Is 0.999... = 1? (spoiler alert: no it is not)

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You may have encountered the popular claim that \( 0.999... = 1 \), where the three dots signify that the decimal continues forever. This is a somewhat weird claim, since it would mean that mathematics is broken. There should be no way for two different numbers to have the same value. What makes it weirder is that this is quite popular claim. I've even seen mathematicians say that it's true! But is it though? One popular proof is to first denote \( S = 0.999...\) and then multiply by \(10\) to get \( 10S = 9.999...\) and subtract \( S \) from it, to get  \( 10S - S = 9.000...\) and finally dividing by \(9\) yields  \( S = 1.000... = 1 \) and we see that  \(0.999... = 1\)! However, there's a problem. This short derivation is not strictly speaking correct. It is veeeery close to being correct, and to see why let's look at finite decimals first. Let's say that \(S = 0.999\) (note that this is not the same as \(S = 0.999...\) ). Let's do the same trick as ...
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The year 2019 in optics and photonics

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Another year, another review. 2019 was quite a wild year for me, and whew, what a decade it has been! It's hard to imagine that at the beginning of the decade, I was still in high school. In chronological order, starting from 2010: I graduated from high school, served in the army, moved across the country, got my BSc, met five Nobel laureates, started a scicomm platform, got my MSc, moved abroad for work, moved back, got my PhD, got married, moved again across the country, and got a postdoc position. I don't think there will be another decade quite like this one for me! What was your year/decade like? Share in the comments! The winner of this years OSA photography contest, by Dr. Pascale Müller and Prof. Dr. Dan Curticapean: the cross section of a bean, imaged with a scanning electron microscope and digitally colored. Anyway, let's get to the sciencey stuff; here are the news that caught my eye from the past year: Nobel prize in physics This years Nobel prize...
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