Question

Two numbers are reciprocals if their product is equal to 1, If x and y are reciprocals and x >1 then y must be?

Answer 1

Any ideas?

Answer 2

less than 1

Answer 3

Correct.

Answer 4

But, there is still one more restriction on y, can you tell me what it is?

Answer 5

$$?\lt y \lt 1$$

Answer 6

less than 0

Answer 7

What goes where the question mark is?

Answer 8

$$\Huge xy=1$$ and x >1 then y must be?

Answer 9

@LilySwan Are you still there?

Answer 10

reciprocals that would +1 and -1 right ?

Answer 11

would what?

Answer 12

The only numbers that are reciprocals of themselves are +1 and -1.

Answer 13

right so that would mean it is less than -1

Answer 14

No.

Answer 15

Numbers that are less than -1 are -1.5, -2, -3, -4,...

Answer 16

so 0

Answer 17

What is zero times any number?

Answer 18

i mean between o and 1

Answer 19

Exactly correct. Between 0 and 1.$$\Huge 0\lt y\lt1$$

Answer 20

that means if x < 1 than y is greater than 0 and less than 1

Answer 21

Does it?

Answer 22

Remember xy = 1 by the definition of a reciprocal.

Answer 23

so than y should also be less than 1

Answer 24

No, x and y just switch roles.

Answer 25

if 0< x <1 then y >1

Answer 26

ok thanks

Answer 27

Thanks for trying to understand this very profound result which says the interval from 0 to 1 can be paired with all the numbers greater than 1...

Answer 28

this number line shows -1>= x or 3<=x

Answer 29

how?

Answer 30

Rather than writing it like you did as " -1>= x or 3<=x" Try to think of it as

x is <= -1 OR x is >=3.

Then x must be in the shaded parts, right?

Answer 31

0<y<1