Question

Show the conjecture is false by finding a counterexample.
1. the quotient of the two whole numbers is a whole number

2. the difference of the abosolute value of the two numbers is positive, meaning...
|a| - |b| >0

3. if m≠ -1 then m *over* m+1 <1

Answer 1

do you know what "counter example" means?

Answer 2

1) 3/8 = 0.375

2) abs(1) - abs(2) = 1 - 2 = -1 < 0

Answer 3

actually no because the teacher kinda just gives us the homework its her first year teaching and she has no clue what shes doing... and were all extremely behind..

Answer 4

ok so we go slow

Answer 5

counter example: say that what you are trying to prove false is true, then use that to find an example to prove it false. (bascially)

Answer 6

the quotient of the two whole numbers is a whole number

a counter example would be two whole numbers whose quotient is NOT a whole number

Answer 7

amost any two whole numbers will do

not \(12\) and \(4\) because \(\frac{12}{4}=3\) IS a whole number, but (12\) and \((5\) would work because \[\frac{12}{5}=2.4\]is NOT a whole number

Answer 8

for
the difference of the abosolute value of the two numbers is positive, meaning... |a| - |b| >0

you have to come up with two numbers \(a,b\) where \(|a|-|b|\) is NOT \(>0\)
in other words, two numbers \(a,b\) where \(|a|-|b|<0\)

Answer 9

that should not be very hard, just pick two numbers where \(b\) is bigger than \(a\)

Answer 10

Okay thank you so much... I'd be lost without openstudy because she expects us to know it after she goes over it once and then when we ask she gets mad at us.

Answer 11

you good with the last one too?

Answer 12

I think so...

Answer 13

what do you need to find? you need to find some number \(m\) so that
\[\frac{m}{m+1}>1\] this might be tricky, maybe not

Answer 14

whole numbers will not work

Answer 15

So find a number thats smaller than it?

Answer 16

find some number \(m\) where \(\frac{m}{m+1}>1\)
\(5\) will not work, because
\[\frac{5}{5+1}=\frac{5}{6}<1\]

Answer 17

so you're saying it will come out to be a decimal but in fraction form?

Answer 18

no let me say it in english
you need to pick a number, so what when you divide that number by a number that is bigger by 1, you get a result that is LARGER than one, not smaller
would you like me to give you an example?

Answer 19

or a hint?

Answer 20

yes please...

Answer 21

pick a number that is negative

any number less than \(-1\) and we can try it

Answer 22

-2

Answer 23

ok so \(m=-2\) and then \(m+1=-2+1=-1\) right?

Answer 24

then \[\frac{m}{m+1}=\frac{-2}{-2+1}=\frac{-2}{-1}=2\]

Answer 25

and there you have it, a COUNTEREXAMPLE, because \(2>1\) not less than

Answer 26

okay thank you so much

Answer 27

yw
that all?

Answer 28

yes you've helped so much thank you

Answer 29

your welcome