Finding Fractional Parts of a Set
5:55
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Finding Fractional Parts of a Set
The fractional part of a set is a portion of a given set of numbers or objects. Using examples, learn to find the parts of a set visually and algebraically.
26K viewsMay 22, 2021
Fractional Part Definition
Letting (x) denote the fractional part of the real number x (see Exercise 16, Chap. 4 , for the definition), consider the function f(x)=∑n=1^∞ ((n x))/(n^2) (x real ) Find all discontinuities of f, and show that they form a countable dense set. Show that f is nevertheless Riemann-integrable on every bounded interval. | Numerade
Letting (x) denote the fractional part of the real number x (see Exercise 16, Chap. 4 , for the definition), consider the function f(x)=∑n=1^∞ ((n x))/(n^2) (x real ) Find all discontinuities of f, and show that they form a countable dense set. Show that f is nevertheless Riemann-integrable on every bounded interval. | Numerade
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