How do I alphabetize an array ignoring case?

I'm using Chris Pine's Learn to Program and am stumped on his relatively simple challenge to take user input in the form of a list of random words and then alphabetize them in an array. Questions about this challenge have come up before, but I haven't been able to find my specific question on SO, so I'm sorry if it's a duplicate.

puts "Here's a fun trick. Type as many words as you want (one per line) and 
I'll sort them in...ALPHABETICAL ORDER! Hold on to your hats!"
wordlist = Array.new
while (userInput = gets.chomp) != ''
   wordlist.push(userInput)
end
puts wordlist.sort

While this does the trick, I'm trying to figure out how to alphabetize the array without case-sensitivity. This is hard to wrap my head around. I learned about casecmp but that seems to be a method for comparing a specific string, as opposed to an array of strings.

So far I've been trying things like:

wordlist.to_s.downcase.to_a.sort!

which, in addition to looking bad, doesn't work for multiple reasons, including that Ruby 2.0 doesn't allow strings to be converted to arrays.

How about:

wordlist.sort_by { |word| word.downcase }

Or even shorter:

wordlist.sort_by(&:downcase)

In general, sort_by is not efficient for keys that are simple to compute. A more efficient comparison is to use sort with a block and replace the default comparison operator <=> with casecmp

wordlist.sort { |w1, w2| w1.casecmp(w2) }

For more information about efficiency gains, consult the official Ruby documentation for the sort_by method: http://www.ruby-doc.org/core-2.1.2/Enumerable.html#method-i-sort_by

I had the same question at my Ruby coding bootcamp. Here's what worked for me:

puts "Type in a sentence."
sentence = gets.chomp.downcase
puts sentence.split(" ").sort