Supply rebuttals to the following complaints about the proof of Theorem 1.5.1.

(a) Every rational numbers has a decimal expansion so we could apply this same argument to show that the set of rational numbers between ° and 1 is uncountable. However, because we know that any subset of Q must be countable, the proof of Theorem 1.5.1 must be flawed.
(b) A few numbers have two different decimal representations. Specifically, any decimal expansion that terminates can also be written with repeating 9's. For instance, 1/2 can be written as .5 or as .4999 Doesn't this cause some problems?

x=-7

step-by-step explanation:

x+3=-10

-10+3=-7

x=-7

5

step-by-step explanation:

d. corresponding side lengths in similar triangles are proportional in length.

step-by-step explanation:

no oblique asymptote

step-by-step explanation:

to find the oblique asymptote of f(x)

here numerator has degree 1 and denomintor degree 2

degree of numerator < degree of denominator

hence there is no oblique asymptote

when the degree of the denominator > that of the numerator, we saw that the value in the denominator got so much bigger, so quickly,   giving us a horizontal asymptote of the x-axis. or we can write

f(x) = a polynomial of x + a proper fraction.

in this case only we have oblique asymptotes but not when numerator has less degree.