Looking it up has gotten me mixed answers. I've seen people refer to either as
the infinitive. A follow-up: is the -ru on ichidan verbs seen as an auxiliary
or is it part of the word?
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grammar linguistics
Is the infinitive form the masu stem or does it include the masu?
Japanese is not an Indo European language. As such, it does not share the same
structures and grammatical concepts. Arguably, Japanese does not have an
infinitive.

What do you mean when you say “infinitive“? Define how you intend the term,
and then we might be able to elucidate whether Japanese has an “infinitive”
for your purposes.
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For what is worth, and always taking into account that it's not the same as an
infinitive, as Eiríkr Útlendi explains in [their
answer](https://japanese.stackexchange.com/a/96582/32952), in Japanese you
have what is sometimes called the "dictionary form". Just like in some
languages such as English and Spanish we look up verbs in a dictionary using
the infinitive, in Japanese you would look up the verb in a dictionary by its
"dictionary form".

For the ichidan verbs, the dictionary form always ends in る, and for the godan
verbs it ends in a mora of the -u (う) column (or row) of the hiragana table,
such as く, つ, む, etc. Whether this final moras of the dictionary form are
regarded as an auxiliary part or as part of the word, I don't know. Does it
really matter? If you look up verbs in the dictionary, they come up as whole
words, including る, く or whatever the ending mora is.

To put it in terms of the "masu stem", you can obtain the dictionary form of a
verb as follows:

  * Ichidan verbs: Add る to the "masu stem".

> たべ ~~ます~~ → たべ → たべ + **る** → たべ **る**

  * Godan verbs: replace the last mora of the "masu stem" by the mora with the same consonant but in the -u (う) column of the hiragana table.

> のみ ~~ます~~ → の **み** → の **む**

This is my personal opinion, but I think that learning verbs and verb
conjugations starting from the masu stem is a mistake, because it just hides
the difference between ichidan and godan verbs, whereas learning verbs
directly in the dictionary form is more natural, and it is very easy to change
from the dictionary form to the masu form.
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