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 0 and 1 is un- countable. 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 . doesn't this cause some problems?

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.

no association

step-by-step explanation:

if you have eyes and you can use them efficiently you can see that it just looks like random dots like do a line of best fit and like they're so spread out it's such a weak association you might as well consider it nonexistent

step-by-step explanation:   divide the numerator by the denominator to get the decimal

it would still be 193

if divide by 100 then 1.93

i am not sure