You can squeeze infinitesimals into hyperreals
“You can’t keep a good idea down!” (as Dr James Grime says in his Numberphile video on the opposite of infinity) Infinitesimals were disposed of, but they came back…
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Nice, and here is the link for a background on early infinitesimals and how they perplexed the learned in Greece… ” Zeno’s dichotomy paradox was the first mathematical concept to consider the relationship between a finite interval and an interval approaching that of an infinitesimal-sized interval.”
More mind-bending miracles with the monad from Numberphile. These guys do all the stuff maths at school didn’t do, and should have.
Agreed, way too late for me now, but if school had chance to inspire us with this stuff who knows which other bright people would have gone into maths and physics and who knows what they would have discovered already – which begs the question, will we discover those missed revalations one day or are they gone for ever. I guess maybe everything gets discovered in the end – but then, that’s another idea that should be on here for people to ponder.
Mathematics doesn’t care if things are real or not real, surreal or hyperreal, what matters is, is it a good tool that lets you get closer to truth. Watch this for a simple description on how they can help people solve difficult problems.
This is the video, not sure if they are ‘really’ there in the real world because of Planck length, but what would I know? Looks like in maths, you can have whatever you like – as long as it isn’t illogical. Hmm.
Maths pinched the word “real” so it doesn’t have to reflect reality. Cheeky, but clever.