Accumulation point of Cantor set
Show that the set of accumulation points of Cantor set is the Cantor set itself?
Real analysis problem with dedekind cuts
A tex-ed pdf document of the problem is attached.
Real analysis problem rational cuts in Q
A tex-ed pdf of the problem is attached. See attached file for full problem description.
How can I show that the cardinality of R and R^2, R=set of Real numbers, is equal. I think by R^2 it is meant R x R, which means an ordered pair, am I right? Is this possible just be showing that the first element in R^2 pair can be matched to R? But this is not necessarily a 'function' by definition, so there are infinite ...continues
Open sets - Prove that a set U subset of M is open
Prove that a set U subset of M is open if none of its points are limits of its complement. I think we may need to use epsilon-delta definitions here. help!
Open interval - The interval (0,1) is an open subset
The interval (0,1) is an open subset of R but not R^2 when we think of R as the x-axis in R^2. Prove this.
Taylor's series of two variables.
Find the Taylor's Series expansion of f(x, y) = sin x sin y about (0, 0).
Taylor's Series for a function of two variables
Find the Taylor's Series for f(x, y) = x^3 + y^3 - 9xy + 27 about (3, 3).
Taylor's Series for a function of two variables
Find the Taylor's series expansion of f(x, y) = sin (e^y + x^2 – 2) around(1, 0).
Taylor's Series for a function of two variables
Find the Taylor's series expansion of f(x, y) = e^x cos y about (a, b).
