1. to avoid doing or having something

2. avoid doing or having something
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It is the definition of 'skip.'
Why is 'to' put before 'avoid'?
Can't we use #2 as the definition of 'skip'?

First of all, I'd need to see 1 and 2 in complete sentences. Context will determine whether "to" can be omitted or not.

And yes, these expressions can mean "skip."
http://www.merriam-webster.com/dictionary/skip

The basis or root of English verbs is the infinitive which is the verb preceded by "to." Most dictionaries use "to" in the definitions of verbs.

Informally, it's fine to omit "to" in a definition.

The word 'to' is used before 'avoid' in the first definition to indicate the infinitive form of the verb. In English grammar, the infinitive form of a verb is used to express purpose or intention. So, in this case, 'to' is used to show that the purpose or intention is to avoid doing or having something.

As for the second question, both the first and second definitions of 'skip' are correct and can be used as the definition of the word. The first definition with 'to avoid' emphasizes the intention to avoid something, while the second definition without 'to avoid' is a more concise way of stating the action of avoiding something. Both versions convey the same meaning, but the first definition provides more clarity and context.