Orders of Infinity, the 'infinitärcalcül' of Paul Du Bois-Reymond

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where A,', S 2 ' are any positive numbers greater than A x and less than S 2 respec- tively. Hence our relation really expresses no more than (1).
22 LOGARITHMICO-EXPONENTIAL SCALES Similarly we can prove that /=e (log»)>- s satisfies (log #) A /' or/-' according as s «'. If s = s', the same relations hold according as r > r' or r /' or/' according as p. > p.' or p. s',s-n' = 0. Putting £„- x=y,we obtain f=e r (l„yT, f=e r .y»'.
If r r\ let r-V=p; then if p > 1 the symbol ^ may
... be replaced by ~. If o- > p, l r f <. l="" r="" f="" and="" so="" if="" o-="" p="" fyf-="">/' or /' according as p.

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