A- Show that if a function is continuous on all of R and equal to 0 at every rational point then it must be identically 0 on all of R
b- if f and g are continuous on all of R and f(r)=g(r) at every rational point,must f and g be the same function?
Solution Preview
a. Proof:
For any irrational point x, we can always find a sequence of rational points x_n such that x_n->x as n->oo. From the definition, ...
Solution Summary
There are two proofs regarding rational points and continuity of functions.
Continuous Functions, Fundamental Set of Solutions. Consider the attached differential equation where I = (a,b) and p,q are continuous functions on I. ...
... and since we take open sets to open sets by well defined we get a continuous function. ... The solution discusses open sets, connectivity and continuous functions. ...
... not continuous at x =0. This posting explains the concepts of limits and continuity in details by providing four examples of functions. 1. Create a function, f ...
... the sup norm | * | on both these sets of bounded functions, for a function f EB(X,R), what, is any, is the relation between |f| and |i* (f)|. Is i* continuous? ...
... Discontinuous Functions Discontinuous functions are functions that are not continuous, that is, not smooth. There are points where the function can't be ...
... variable is defined over a continuous range of values (called the domain of the variable), the graph of the density function will also be continuous over that ...
... control engineer has been checking the output by almost continuous sampling since ... The probability density function of binomial random variable is given by P(X=x ...
... probabilities are given by areas under the curve or graph of the probability density function f(x ... Since continuous probability functions are defined ...
... Time Compounding $7500 $15,877.50 15 years Continuous. ... the Practice Questions on Logarithmic and Exponential Functions. ... the graph of the function and identify ...
