> > By the standard limit-based definition of an infinite sum, > > 1 + 1/2 + 1/4 + 1/8 + ... equals 1, exactly > > Once again, this is old knowledge -- thousands of years old.
Yup. Even old Zeno could not undo it. > > If you won't allows limits to be regarded as real numbers, you lose a > lot of math and science. Your conservatism is too costly in terms of > all the wonderful (and useful) mathematical and scientific theories > that you won't be able to accept.
Without limits and convergences one has a very feeble system of mathematics which is fit only to tally up grocery bills.
Forget about integrals. Forget about solving differential equations. Forget about doing physics.