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I have come across the word infrequent in the patient information leaflet for Prozac. When looking up the German translation of that word, I wondered what exactly is the difference between infrequent and rare?

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    infrequent indicated what relationship between time and events. and rare` just mean not too much. – Frank AK Jul 4 '18 at 10:53
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First, the definitions:

Infrequent: Oxford

Not occurring often; rare.

and

Rare: Oxford

  1. (of an event, situation, or condition) not occurring very often.

    1.1. (of a thing) not found in large numbers and so of interest or value.

    1.2. Unusually good or remarkable.

From the definitions, we see that both rare and frequent can both refer to something that does not occur very often.

However, rare can also refer to something which does not exist in large numbers, such as works of art or certain species of creature.

So you can say that supernovae are rare or supernovae are infrequent. However, while you can say that the Philippine Eagle is rare, you cannot say it is infrequent.

EDIT: As pointed out in the comments by @JasonBassford, when used to express frequency, rare would be more appropriate in more extreme cases.

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    Based purely on those definitions, something infrequent doesn't occur often while something rare doesn't occur very often. Although synonymous, it could be argued (and it seems intuitive to me) that rare is the more extreme of the two. – Jason Bassford Jul 4 '18 at 14:29
  • I would argue against that: infrequent itself includes 'rare' as one of its definitions, therefore any extremity of frequency would be equal. – John Go-Soco Jul 4 '18 at 14:39
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    Something can be synonymous to something else while still having a different specific meaning. Among five different synonyms for example, frequently only one of them is the exact word you want to use. Dictionary definitions often provide synonyms; that doesn't mean that the synonyms are identical . . . – Jason Bassford Jul 4 '18 at 15:29
  • Shouldn't you be writing "From the definitions, we see that both rare and infrequent" instead of "From the definitions, we see that both rare and frequent". – Norbert Willhelm Jul 4 '18 at 17:30
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    @JasonBassford Actually, I think you've won me over. On reflection, I would also even agree with you that intuitively, I would use 'rare' as a more extreme case, but I guess my point was that one could not take that sense from the definitions, but more from real-world usage and experience. – John Go-Soco Jul 5 '18 at 7:18

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