I don’t know if this is just me, but it took me an embarrassingly long time in my mathematical education to realize that the following three terminologies, which introductory textbooks used interchangeably without being explicit, mean the same thing. (Maybe this is just because English is my second language?)
For some reason the “only if” always throws me off. It reminds me of the unless keyword in ruby, which is equivalent to if not, but somehow always made my brain segfault.
I think the interchangeability is just hard to understand. Even though I know they are the same thing, it is still really hard to intuitively see them as being equal. I personally try (but not very hard) to stick with X → Y in mathy discussions and if/only if for normal discussions
I don’t know if this is just me, but it took me an embarrassingly long time in my mathematical education to realize that the following three terminologies, which introductory textbooks used interchangeably without being explicit, mean the same thing. (Maybe this is just because English is my second language?)
For some reason the “only if” always throws me off. It reminds me of the
unlesskeyword in ruby, which is equivalent toif not, but somehow always made my brain segfault.Saying “if X then Y” generally is equivalent to “X is sufficient for Y”, “Y is necessary for X”, “X only if Y”.
I think the interchangeability is just hard to understand. Even though I know they are the same thing, it is still really hard to intuitively see them as being equal. I personally try (but not very hard) to stick with X → Y in mathy discussions and if/only if for normal discussions