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"Each of the first ten whole numbers is written on a card."

The sentence will be used to support the following question:

Find the probability that a card taken at random has a label of an even number.

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3 Answers

up vote 1 down vote accepted

"The [ten] numbers 1 to 10 are written on one card each."

(That would be my suggestion; other alternatives may be "Each of the numbers 1 to 10 is written on a separate card", or even "The ten numbers 1 to 10 are written on ten cards, one number on each card.")

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Good alternatives!!! – xport Oct 14 '10 at 7:56
"...on one card ..." "... on a card", is there a difference in nuance between "one card" and "a card"? – xport Oct 14 '10 at 8:06
@xport: I don't think there's much difference between them; they're mostly the same. – ShreevatsaR Oct 14 '10 at 8:33
up vote 1 down vote

There is a card with a number for each whole number from 1 to 10.

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up vote 1 down vote

Maybe not relevant for spoken language or non mathematical settings, but the term whole number is ambiguous. In this case I think you mean the natural numbers or non-negative integers, starting at 1 ( {1,2,3,4...} ). Whole numbers (usually including the negative integers as well) do not have a notion of first, unless you define an order to them like { 0, 1, -1, 2. -2, ...}, used to show their countability.

But to your question. I would phrase it like this (edited based on comments):

The numbers 1 through 10 are written on a card each.

or

There are ten cards numbered 1 to 10, one number on each card.

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3  
+1 for "There are ten cards numbered from 1 to 10." Very simple and very clear. – b.roth Oct 13 '10 at 15:38
-1: I don't think 'whole numbers' is ambiguous, because, while negative integers are whole, nobody would dispute that the most obvious interpretation of 'the first ten whole numbers' is the numbers one through ten. If the context were formal mathematics, I would agree with your assessment, but it sounds like it is from a more elementary/informal context than that, for which 'whole numbers' is perfectly valid. I like Bruno's answer. One example sentence for my interpretation: 'Integers are the whole numbers, negative whole numbers, and zero.' – J D OConal Oct 14 '10 at 5:02
@Ralph,"There are ten cards numbered from 1 to 10" can also incorrectly be interpreted as follows: There are ten cards, each is labeled with 10 numbers from 1 to 10. – xport Oct 14 '10 at 5:04
1  
@J D OConal: According to what many students are taught in school (differs from school to school), the whole numbers are defined to be the set {0, 1, 2, …} (the set {1,2,3…} is called the natural numbers), and with such a definition "the first ten whole numbers" unambiguously means 0, 1, 2, … 9, not 1 to 10. (The ambiguity is because other definitions exist.) Especially in the context of a probability question on a test (which seems to be the context here), not using things according to their definition will cause a lot of trouble. – ShreevatsaR Oct 14 '10 at 7:15

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