
Real Numbers
Hi,
Someone give me a hand in checking these please.
a.) Given that , and for the real numbers , and , show that .
...1
is +ve...2
...3
If then is +ve
Putting values using lines 2 and 3
OR
...................OR +ve
therefore must be true
b.) Show that if x, y ∈ R, and , then for any real number , .
...1
is ve
...3
If then is ve
Putting in values using lines 2 and 3
.......................OR
................OR
therefore must be true

Quote:
Originally Posted by
Hellbent a.) Given that
, and
for the real numbers
,
and
, show that
.
...1
If x = 3, y = 2, and k = 1, then kx = 3, which is less than y. So your last line above cannot be assumed always to be true.
Try starting like this:
Let x > y, and let k < 0. Assume that kx > ky. Then kx  ky > 0. Also, kx  ky = k(x  y). Since x > y, then x  y > 0.
See where this leads.... (Wink)

Am I right this time?
a.) Since x > y, so x  y is positive and k is negative.
Product of a negative and positive number is negative, kx  ky
Hence it follows that kx < ky.
b.) Since x < y, so x  y is negative and k is negative.
Product of two negative numbers is equal to a positive number.
Hence it follows that kx > ky.


Quote:
Originally Posted by
Hellbent Right...wrong?
it seems right for me.(Nod)

is strictly positive.(Nod)