Split an infinitive
Definition 1 of 1
Pro Tip 1/3Style Choice
Split infinitives can stylistically emphasize the action, but may be frowned upon in formal writing. 
He decided to not participate in the event.
Pro Tip 2/3Rhythmic Flow
Adding an adverb can create a natural rhythm making the phrase easier or more pleasing to hear. 
She learned to quickly adapt to new situations.
Pro Tip 3/3Cultural Icon
The Star Trek example shows that famously split infinitives can become iconic in popular culture. 
The phrase 'to boldly go' is recognized worldwide thanks to Star Trek.