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A mixed fraction is an improper fraction p/q>1 written in the form n+r/s. In common usage such as cooking recipes, n+r/s is often written as n r/s (e.g., 1 1/2), much to the ...

A necessary and sufficient condition that [alpha^'] should be comparable with [alpha] for all positive values of the a is that one of (alpha^') and (alpha) should be ...

For b>a>0, 1/b<(lnb-lna)/(b-a)<1/a.

If f(x) is a monotonically increasing integrable function on [a,b] with f(b)<=0, then if g is a real function integrable on [a,b], ...

A theorem stated in 1882 which cannot be derived from Euclid's postulates. Given points a, b, c, and d on a line, if it is known that the points are ordered as (a,b,c) and ...

The use of permil (a.k.a. parts per thousand) is a way of expressing ratios in terms of whole numbers. Given a ratio or fraction, it is converted to a permil-age by ...

The use of percentages is a way of expressing ratios in terms of whole numbers. A ratio or fraction is converted to a percentage by multiplying by 100 and appending a ...

The use of permil (a.k.a. parts per thousand) is a way of expressing ratios in terms of whole numbers. Given a ratio or fraction, it is converted to a permil-age by ...

Let f(z) be an analytic function in an angular domain W:|argz|<alphapi/2. Suppose there is a constant M such that for each epsilon>0, each finite boundary point has a ...

A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived. The whole of ...