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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3It’s undefined. – Brian M. Scott Jun 22 '12 at 14:02
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1possible duplicate of Division by zero, or one of these other fine results – MJD Jun 22 '12 at 14:08
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1Also closely related: http://math.stackexchange.com/q/43251/622 – Asaf Karagila Jun 22 '12 at 14:10
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6@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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1@WillieWong I think the same way. – Jun 22 '12 at 14:20
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@Willie: As far as I’m concerned, ratios are fractions, merely expressed in a different notation. And if I were to speak informally of the ratio of boys to girls in groups with no girls, I definitely would not say that a ratio of $1:0$ is the same as a ratio of $2:0$. – Brian M. Scott Jun 22 '12 at 14:59
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1@BrianM.Scott: How would you express the odds agains an impossible event, for example (say, with a finite sample space)? – Cameron Buie Jun 22 '12 at 18:15
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@Cameron: I wouldn’t. I’d say that the probability is $0$. – Brian M. Scott Jun 22 '12 at 18:18
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@Brian: As would I, given my preference, but if a student were given a problem in which they were requested to express such odds, how would you advise them? – Cameron Buie Jun 22 '12 at 18:21
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1@Cameron: That it’s a bad problem, and that they should say so. – Brian M. Scott Jun 22 '12 at 18:26
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@Brian: lol Fair enough! – Cameron Buie Jun 22 '12 at 18:31
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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.
Glorfindel
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Cameron Buie
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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).
nullUser
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Defined, but arbitrary, yes? If it all reduces to zero, the ratio of girls to boys is 0:1 and 0:30 and 0:1000000. Seems fishy. – nasch Dec 09 '22 at 16:41
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@nasch This is defined and in my opinion not arbitrary at all, but you bring up an excellent point in that the ratio of boys to girls does not give any information about the total number in each group. A ratio of 0 girls to 30 boys is equal to a ratio of 0 girls to 100000 boys, which is different information than the information that there were 0 girls and 30 boys versus 0 girls and 100000 boys. The ratio conveys strictly less information, since ratios can always be computed from totals but totals cannot be computed from just the ratio. – nullUser Jun 01 '23 at 18:45