No, that isn't the case. "To be" is the verb in that case, and "into" remains a preposition. I do have a separate question, though. Would there ever be a reason to use "in to" rather than "into?"--Pirsqed16:07, 23 August 2006 (UTC)Reply
I'd guess that there are cases where a verbal phrase includes "in", which might be followed by "to" as a separate preposition, though I can't think of a good example. Also, of course, any place where "to" should occur as part of an infinitive verb it would be incorrect to use "into": "He goes in to eat." --Xyzzyva22:55, 27 November 2007 (UTC)Reply
My favorite illustration of the difference betweenin to andinto is "I brought the cake in to my mother" vs. "I pushed the cake into my mother". —Aɴɢʀ (talk)10:02, 12 January 2014 (UTC)Reply
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7.(mathematics) Taking distinct arguments to distinct values.
The exponential function maps the set of real numbersinto itself.
I haven't been able to find clear verification that this definition is technically correct (leaving aside for the moment the fact that this is not strictly the definition of a preposition and should probably be converted to "non-gloss"). In fact, two places where I have found this sense of "into" explained,[1] and[2], both seem not to support it, as far as I can tell. I don't feel qualified to judge this. Does anyone know for sure?Mihia (talk)20:38, 5 September 2020 (UTC)Reply
The given definition is that of aninjective function. While the termonto is commonly used in mathematical parlance for the dual notion of asurjective function – even as an adjective – the terminto has no similar status. It is the preposition of choice for the special case ofinclusion maps, which are injective functions – but probably not so much that it attains lexical status. The usex suggests a sense of ”not surjective“, which is also how the first place linked to above defines it, and it is perhaps also sometimes used that way. The second place linked to defines it as a synonym ofto, which I think is more common than specifically excluding surjections. Inclusion maps are normally not surjective, but this is not essential to their mathematical definition; theidentity function is surjective and trivially also an inclusion map. --Lambiam08:27, 6 September 2020 (UTC)Reply
Thanks for looking at this. In this instance, I'm afraid I will have to leave it to you and/or others to determine whether we need a mathematical definition for "into", and, if so, how it should read.Mihia (talk)22:08, 6 September 2020 (UTC)Reply
I think we don't need one for a presumed mathematical meaning of the preposition when used for marking the range of a function (“a function fromA intoB ”), because it does not have a specific mathematical meaning in such uses. As usedhere,here andhere it is synonymous withto, which it also is in the lead of the Wikipedia articleFunctional (mathematics) and in countless other places. --Lambiam15:36, 9 September 2020 (UTC)Reply
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According to Swan'sPractical, after some verbs (e.g.,throw jump, push, put, fall) we can use bothin andinto, oron andonto, for directional movement. We preferinto/onto when we think of the movement itself, and in/on to emphasize the end of the movement - the place where somebody or something will be:These kids keep jumpinginto the flowerbeds. Go and jumpin the river!JMGN (talk)09:21, 12 June 2025 (UTC)Reply
In formal written English, inward movement withinto, not in:welcomedinto the family. Using in forinto can be misleading, as in I jumped in the pool (jump into it vs standing in when I did).JMGN (talk)10:25, 8 July 2025 (UTC)Reply
