That makes a lot more sense! Actually rings a bell from when I ran in to the same wrongly-remembered wording in uni.
I'm not sure why, but getting back to the right terminology/vocabulary just to get back in to the basics of mathematics is a lot harder for me than it was 20 years ago.
If you casually want to get into it without the commitment, I've found that even passively watching the Tim Roughgarden videos from Coursera (probably can be found crossposted to YouTube by third parties) to be stimulating in the past.
If you seek to acquire formality and rigor, I can't help you there; I figure shortcuts will be nonexistant ;)