Question

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

Answer 1

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

Answer 2

yea for the most part

Answer 3

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

Answer 4

ok thanks!

Answer 5

so going by that can you figure it all out?

Answer 6

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.

Answer 7

thattt is totally what i said -.-

Answer 8

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

Answer 9

Some books consider 0 \[0 \in \mathbb{N}\]

Answer 10

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

Answer 11

that would be called integers are all real numbers

Answer 12

which are all*** real numbers

Answer 13

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

Answer 14

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

Answer 15

There are infinitely many irrationals between 0 and 1 =o

Answer 16

I really digressed from the main question. I apologize.

Answer 17

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