## anonymous 5 years ago 1. The difference of two natural numbers is always an integer. 2. The difference of two natural numbers is always a natural number. 3. The sum of two natural numbers is always a natural number. 4. The product of two natural numbers is always a natural number. 5. The quotient of two natural numbers is always a rational number 6. The quotient of two natural numbers is always a natural number. 7. The ratio of two natural numbers is always positive I need help determining which ones are true and which are false

1. anonymous

do you know the different between real, rational, natural, etc numbers?

2. anonymous

yea for the most part

3. anonymous

ok well just to quickly go over them: natural numbers are 1, 2, 3, 4, 5, 6, they are positive and whole rationals are simply decimals or fractions that can be expressed as a fraction: aka they do not go on forever without repeating. so 2/3 or .6666666... or simple ones like 1/4 integers are + or - whole numbers

4. anonymous

ok thanks!

5. anonymous

so going by that can you figure it all out?

6. anonymous

no natural numbers are all the positive number without decimals and zero. Rational numbers are numbers that can be expressed in a ratio or quotient of natural numbers.

7. anonymous

thattt is totally what i said -.-

8. anonymous

rational numbers are however numbers with repeating decimals like 3.33333 and 2.252525

9. anonymous

Some books consider 0 $0 \in \mathbb{N}$

10. anonymous

right, i see the confusion when i said "without repeating" i meant, they must repeat if they go on forever

11. anonymous

that would be called integers are all real numbers

12. anonymous

which are all*** real numbers

13. anonymous

Rational numbers are simply numbers that can be expressed as $\frac{a}{b} a,b \in Z$

14. anonymous

Defining the REALs is tricky business. And requires Analysis to grasp. There are tiny holes between any two rationals numbers. These tiny holes are irrational numbers. Which can be said to be "non-terminanting without repeating decimals" as Kynosis put it. We have to patch up these holes to "COMPLETE" the REALS

15. anonymous

There are infinitely many irrationals between 0 and 1 =o

16. anonymous

I really digressed from the main question. I apologize.

17. anonymous

1. The difference of two natural numbers is always an integer. True 2. The difference of two natural numbers is always a natural number. False 3. The sum of two natural numbers is always a natural number. True 4. The product of two natural numbers is always a natural number. True 5. The quotient of two natural numbers is always a rational number True 6. The quotient of two natural numbers is always a natural number. False 7. The ratio of two natural numbers is always positive True