What exactly do TDS readings after RO/DI filtration tell you?

[jonboyb]

While I was forced through chemisty in school and have become much better since reefing, a newbie recently posed a question I couldn't completely answer.

If your fresh water measures at 0 TDS, what else might you have to worry about?

Does calcium, magnesium, and other ionic trace make it through filtration?

Can 0 TDS water still harbor nitrates and phosphates?

I've been reefing for a year and into SW aquariums much longer but I've honestly never stepped back and thought about exactly what RO/DI filtration removes. Yet here was a literal complete SW newbie and this was one of his first question

 

[jonboyb]

His line of questioning was more wanting to know if he's getting a TDS of 0 is there ANY need to worry about other things. Nitrates, phosphates, trace, etc or does RD/DI filtration strip everything out.