Yes, you're right -- but you missed the second infinitive phrase: "to count."
"To count" is also a noun because it's the direct object of "learn."
Can you tell me what words are the infintive phrase and is it a noun, adj or adv? Is it To learn and it's a noun?
To learn to count in three languages is my summer goal.
2 answers
"To learn to count" is an infinitive phrase used as the subject of the sentence. In the phrase," to count" is an infinitive direct object of "to learn".