1 + 2 + 4 + 8 + ⋯ that and , but the underlying proofs demand careful thinking about the interpretation of endless sums. It is also possible to view this series as convergent in a number system different from the real numbers, namely, the 2-adic numbers. As a series of 2-adic numbers this series converges to the same sum, −1, as was derived above by analytic continuation. 1 + 2 + 4 + 8 + ⋯ In mathematics, is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2.
Minim (unit) size of a drop can vary considerably depending upon the viscosity and specific gravity of the liquid. (At the time, the phenomenon of surface tension was not well understood.) The minim, on the other hand, was measured with a graduated glass tube known as a "minimometer", later known as the minim-tube. The minim-tube was a type of graduated pipette, a device invented in 1791 by François-Antoine-Henri Descroizilles. Apothecaries' measures are fully defined in the United Kingdom's Weights and Measures Act of 1878, but the UK's 1963 Weights and Measures Act provided for the abolition of the minim, fluid scruple, and