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What is the ratio between boys and girls in a group with 30 boys and 0 girls? Is it 1:0, 30:0 or something involving infinity and undefined?

Can somebody help me out here?

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It’s undefined. –  Brian M. Scott Jun 22 '12 at 14:02
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possible duplicate of Division by zero, or one of these other fine results –  MJD Jun 22 '12 at 14:08
    
Also closely related: math.stackexchange.com/q/43251/622 –  Asaf Karagila Jun 22 '12 at 14:10
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@Brian: is it really though? I prefer to identify ratios not with fractions, but with something like projective space: I would say that for any two (nonempty) groups of children with no girls, the ratio of boys to girls are the same. Only in the case of $0:0$ would I really think that the ratio is undefined. –  Willie Wong Jun 22 '12 at 14:17
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@Cameron: That it’s a bad problem, and that they should say so. –  Brian M. Scott Jun 22 '12 at 18:26

2 Answers 2

up vote 3 down vote accepted

Here is a discussion on the topic. I tend to agree with Willie, myself, and would in this case say that it was $1:0$--in words, "for every boy in the group, there is no girl in the group"--which, thought of in this way, would be conceptually the same as $30:0$, but "reduced". Evidently, though, there is disagreement on this issue. My recommendation is that you try to determine which view is espoused by your text(s) and instructor(s), and stick by that.

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As was mentioned by others, it is undefined. If you want the ratio "of A to B" then this means you want $|A|/|B|$. E.g. the ratio of Boys to Girls is the number of boys divided by the number of girls. Hence, the ratio makes sense if and only if $|B|$ is not zero, since division by 0 is undefined.

Note: this means the ratio of 30 boys to 0 girls is undefined, but the ratio of 0 girls to 30 boys is defined (and is 0).

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