Question

Which of the following is a counterexample of, "All rational numbers are integers"?

is not an integer.
3 is an integer.
-1 is a rational number.
π is a rational number.

Answer 1

what is the ? asking

Answer 2

pi is not a rational # i dont think

Answer 3

so i believe d can b eliminated

Answer 4

oh i for got to add \[\frac{ 1 }{ 2 }\] in front ofther first option

Answer 5

but what is the ? asking

Answer 6

i think its to show its a question not a statement

Answer 7

by counterexample, it means on the contrary, correct?

Answer 8

i thinik...

Answer 9

Hey Audie :)
"ALL rational numbers are integers"

To show a counter example:
Find a rational number which is NOT an integer.
That will contradict the ALL of the original statement.

Answer 10

i uh dont no what a integer is... @zep

Answer 11

or i do and forgot

Answer 12

an integer is a positive or negative whole number, or zero.

Answer 13

What is an integer?
Mathematically, integers are set of whole numbers (including zero), and the negative whole numbers: {0, 1, 2, 3, 4, ...} + {-1, -2, -3, -4, ...}
In programming, an integer is limited to 32 bits of information, from -2,147,483,648 to 2,147,483,647.

Answer 14

an integer can pretty much be any number

Answer 15

so c then?

Answer 16

Notice that the 4th option is clearly false.
pi isn't a rational number.
we don't care about the set of irrational numbers, the statement has nothing to do with them.

Answer 17

-1 is a rational number.
I'm saying that -1 is also an integer.

Hmm, nope. That supports the statement. It doesn't contradict it.

Answer 18

i dont think it could be a because thats 1/2

Answer 19

is 1/2 a rational number?
is 1/2 an integer?

Answer 20

its not a integer because it says that but i dont think its rational because you cant rationalize it

Answer 21

a rational number is a number which can be written as a ratio of integers.

Example:
5/2 is a rational number because it's an integer on top and on bottom.
0.15 is rational because we can write it as \(\large\rm \frac{15}{100}\). Again a ratio of whole numbers.

Answer 22

oh so it would be a then...

Answer 23

So you've determined:
1/2 is a rational number
1/2 is not an integer

Therefore ALL rational numbers cannot possibly be integers.
Yessss good job \c:/

Answer 24

thank you for your help!