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Which set includes rational numbers but not natural numbers?



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(1 point)
Responses

34, 456, 185, 8
34, 456, 185, 8

−5, −4, 4, 5
−5, −4, 4, 5

−623, −2, 511, 78
−623, −2, 511, 78

0, 1, 2, 3

5 answers

To find the set that includes rational numbers but not natural numbers, let's first define the two types of numbers:

  • Natural Numbers: These are positive integers starting from 1 (1, 2, 3, ...). They do not include negative numbers or zero.
  • Rational Numbers: These are numbers that can be expressed as a fraction (where the numerator and denominator are integers, and the denominator is not zero) and include integers, fractions, and whole numbers, both positive and negative.

Now, let's analyze the given sets:

  1. 34, 456, 185, 8 - All positive integers (natural numbers).
  2. −5, −4, 4, 5 - This set includes negative integers (−5, −4) and a positive integer (4, 5). All are rational numbers, but no natural numbers are included.
  3. −623, −2, 511, 78 - This set includes negative integers (−623, −2) and positive integers (511, 78). Like the previous set, this contains rational numbers but also includes natural numbers (511, 78).
  4. 0, 1, 2, 3 - Zero and natural numbers. This set includes both.

Based on this analysis, the set that includes rational numbers but not natural numbers is:

−5, −4, 4, 5

wrong

I apologize for the oversight. Let's reevaluate the answer carefully. We are looking for a set that contains rational numbers, but specifically excludes natural numbers.

  • Natural numbers: {1, 2, 3, ...}, so any set that contains these is not a valid choice if we're excluding natural numbers.

Now, let’s go through the options again:

  1. 34, 456, 185, 8 - All positive integers (natural numbers) — NOT a valid choice.

  2. −5, −4, 4, 5 - This set contains negative integers and one positive integer (4, which is a natural number). — NOT a valid choice.

  3. −623, −2, 511, 78 - Contains negative integers (−623, −2) along with positive integers (511, 78). — 511 and 78 are natural numbers — NOT a valid choice.

  4. 0, 1, 2, 3 - Contains zero (which is not a natural number) and natural numbers (1, 2, 3) — NOT a valid choice.

Based on the above analysis, it appears you need a set that comprises rational numbers without including any natural numbers.

Given the context again, one correct answer could have been a choice encompassing negative numbers or zero alone without positive integers.

However, based on the provided options, none fit perfectly. The closest option that generally aligns with containing rational numbers but cannot be classified strictly is \(-5, -4, 4, 5\), because it still relates back to rational numbers excluding negative integers.

If we strictly abide by your criteria and must select based on the options, I apologize for any confusion. Please check with your platform's assessment or questions regarding the propriety of the question items. Thank you for your understanding.

whats the closest answer

Given the options provided and the requirement to find a set that includes rational numbers but not natural numbers, the closest answer would be:

−5, −4, 4, 5

While this set does include the positive integer 4 (which is a natural number), it also contains two negative integers (−5 and −4), which makes it the best option among the provided choices in terms of containing rational numbers, as the other options either contain only natural numbers or include only natural numbers along with zero.

So, if forced to pick from the given choices, −5, −4, 4, 5 would be the best option, even though it technically doesn't fully meet the requirement because it includes the natural number 4. Thank you for your patience.