What's the difference between the infinitive, bare infinitive and base form?

The base form is that form of the verb that usually appears in the dictionary. It is the form from which all other parts of a regular verb are constructed. For example, WORK is the base form of the verb; from it we can construct the forms works, working and worked.

The base form is used unchanged for the first and second persons singular and all plural forms of the present simple of all verbs except BE. It is also used for the bare infinitive (the form which, for example, follows the modals - he can work), the imperative and, for those who use it, all persons of the present subjunctive. The to- infinitive is a form consisting of the particle to and the bare infinitive; It has a variety of uses as in, for example, I want to work, It is pleasant to work, To work for a top accounting form is the dream of many young accountants.

In all your sentences, the bare infinitive travel is used

In English, verbs aren't commonly described as infinitives except by people who are learning English as native speakers of another language (especially Romance languages) or by people who are obsessed with Latin. When people do talk about English infinitives, they're talking about verbs that take their simple, present tense forms and do not have a definite duration. For example:

• I want to go to Florida.
• To resist is futile.
• I could read all day!

The infinitive structure comes to us courtesy of Latin, and its useful to English language learners because many Romance languages employe the structure. For example, verbs in Spanish have actual infinitive forms that get used in specific circumstances in Spanish grammar, like when you talk about something that pleases you. When I say in Spanish, "Me gusta jugar a baloncesto," what I'm literally saying in English is, "To play basketball pleases me." This sounds odd in English because we don't use infinitives the same way Spanish speakers do, but in Spanish, this kind of sentence construction is common.

In your examples, all of your sentences are using "travel" as an infinitive, but trying to figure out why will probably confuse you for no good reason. Learning how to analyze sentences can help you identify infinitives, but learning how to identify infinitives will almost certainly not benefit you in any meaningful way simply because we don't use infinitive structures consistently in English.

Here are the answers to the questions in your title:

• The infinitive form of a verb, in English, is the form of the verb used to describe action of a non-finite duration, possibly with the word "to" attached to it, as with "to go", "to play", or "to study".
• The bare infinitive form of a verb is the same as the infinitive form, only without the word "to".
• The base form of a verb is incidentally the same as the infinitive--the form of the verb used to describe action of a non-finite duration, without "to". We use the phrase base form to describe something different, though. A verb's base form is the form of the verb that has no special endings. You'll find verbs listed in the dictionary by their base forms. "Go" is a base form, but "went" is not. "Play" is a base form, but "to play" is not. "Study" is a base form, but "studies" is not. When you see a base form of a verb in writing, it's probably either acting as a first or second person singular verb ("I go," "You go,"), a plural present tense verb ("We go," "They go,"), and/or an infinitive. Base forms of verbs can be infinitives, but they aren't always.

Alex, your Question was: Can you please give me and example or two where the base form of the verb is used and yet can not be considered as an infinitive?

This is a good question and one that I had been wondering about. The infinitive "to play" without the word "to" is called a bare infinitive. The bare infinitive and the base form are pretty much the same thing.

Examples:

"I play in the yard." - base form

"I want to play in the yard." - infinitive form

As was mentioned before, the base form is seen in dictionaries. The word is listed by itself without being in a sentence. For instance the word "Play" would be in the dictionary by itself. After the word, the dictionary may show its uses in a sentence, but it initially simply puts the word out alone. Here it could be said that we are thinking of the base form.

As was mentioned before by R Mac on Nov 11, 2014 - we often think of the infinitive when we are learning languages like Spanish or English for the first time. The word "play" can be a verb or a noun. In a language learning dictionary, the word "Play" might be put out as "Play (to)" or "Play". In a language learning dictionary, they write in "Play (to)" because it is a quick way to let learners know that this is the verb: "to play". They do this so that it can not be confused with the noun "play" (or "a play"). In this instance "Play (to)" is thought of as an infinitive and not a base form.