Solution 1:

You might see the infinitive is the form of the verb that has most of the following features:

  • it is the form that does not carry any of the inflections that essentially any "productive" verb can carry that restrict the interpretation of that verb;
  • it is the form that can be the complement of a modal auxiliary;
  • it is the form that may be specified by a special selection of prepositions (sometimes called "pre-infinitival prepositions": "to" in English, "zu" in German, "de" in French etc).

Beware of just saying that the infinitive is the form "without inflection", because some languages have specific endings/inflections that are actually added to the root to specify "infinitive", and infinitives may allow certain modifications e.g. to mark perfective aspect in Slavic languages, to mark reflection/voice in various European languages. They're the form "without inflection" so long as you understand "inflection" in a particular way.

Solution 2:

The infinitive is the basic or root verb form, uninflected.

For example, in "to work" the infinitive is "work":

We didn't come here to have fun, we came here to work.

Other forms are derived from the infinitive:

I worked.

He works.

You'll usually find me working.

And so on.

Solution 3:

The Cambridge Grammar of the English Language defines an infinitive thus:

Those with a plain form are infinitival, and are subdivided into to-infinitivals and bare infinitivals depending on the presence or absence of the VP [verb phrase] subordinator to.

  1. It was Kim's idea to invite them all. [to-infinitival]
  2. She helped them prepare their defence. [bare infinitival]

Solution 4:

Verbs are used various different ways:

We invite friends over every night. It is fun. (present tense)

We invited Kaitlin. She was busy though. (past tense)

We are inviting someone new. He likes being the center of attention. (-ing form)

The infinitive is another way to use a verb. In English, the easiest ways to identify the infinitive are

  • the word to usually comes before the verb phrase;

  • the verb does not take a suffix -s, -ed, or -ing, and in particular, the word be can be used as the verb, rather than is, was, or being.

We don’t want to invite him. He likes to be the center of attention. (infinitive)

The infinitive can't be the main verb of a sentence. It often comes after another verb, like want or likes above. But not always:

To invite her would be a mistake. (infinitive as subject)

This is another way to use the infinitive. (infinitive after way)

The infinitive appears without to in a few places, particularly after the modal auxiliary verbs can/could/may/might/will/would/shall/should/must and after a few other verbs like help.

He can be the center of attention if that’s what he wants. (infinitive after can)

Help me invite all these people to our party. (infinitive after help)