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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

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  1. anonymous
    • 5 years ago
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    do you know the different between real, rational, natural, etc numbers?

  2. anonymous
    • 5 years ago
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    yea for the most part

  3. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    ok thanks!

  5. anonymous
    • 5 years ago
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    so going by that can you figure it all out?

  6. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    thattt is totally what i said -.-

  8. anonymous
    • 5 years ago
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    rational numbers are however numbers with repeating decimals like 3.33333 and 2.252525

  9. anonymous
    • 5 years ago
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    Some books consider 0 \[0 \in \mathbb{N}\]

  10. anonymous
    • 5 years ago
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    right, i see the confusion when i said "without repeating" i meant, they must repeat if they go on forever

  11. anonymous
    • 5 years ago
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    that would be called integers are all real numbers

  12. anonymous
    • 5 years ago
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    which are all*** real numbers

  13. anonymous
    • 5 years ago
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    Rational numbers are simply numbers that can be expressed as \[\frac{a}{b} a,b \in Z\]

  14. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    There are infinitely many irrationals between 0 and 1 =o

  16. anonymous
    • 5 years ago
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    I really digressed from the main question. I apologize.

  17. anonymous
    • 5 years ago
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    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

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