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Hmm interesting … I would've said that without a doubt, unless Cantor, Godel, Boltzman, Turing, etc formalised thinking about dimensionality, as it relates to the concept of infinity, then vast amounts of technologies and development would never have happened.
Solutions to pdes are bread-and-butter housekeeping in engineering projects !
Barry's assertion that infinity has been assigned meaning is fine by me, if it has ultimately resulted in tools which reinforce the theory everytime I turn on my computer, use a phone, go for an NMR/MRI etc, etc …
Cheers
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