anonymous one year ago 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.

1. anonymous

2. anonymous

pi is not a rational # i dont think

3. anonymous

so i believe d can b eliminated

4. anonymous

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

5. anonymous

but what is the ? asking

6. anonymous

i think its to show its a question not a statement

7. anonymous

by counterexample, it means on the contrary, correct?

8. anonymous

i thinik...

9. zepdrix

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.

10. anonymous

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

11. anonymous

or i do and forgot

12. zepdrix

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

13. anonymous

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.

14. anonymous

an integer can pretty much be any number

15. anonymous

so c then?

16. zepdrix

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.

17. zepdrix

-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.

18. anonymous

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

19. zepdrix

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

20. anonymous

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

21. zepdrix

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.

22. anonymous

oh so it would be a then...

23. zepdrix

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:/

24. anonymous