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So I like the presentation. But I can't get past the first puzzle. The hints don't really help. Is there a walkthough?

There is no walkthrough for the demo. If you still need another hint: when you figure out what is the synonym of "nothing" based upon the second hint, the solution should become clearer.

Sorry, but it doesn't. Every synonym I can think of, of nothingness based on the idea of "increment" doesn't make a word/phrase in the box. I'm trying, but it's just not making sense to me. It's just a shame if there's no answer key since  it cuts me off from the rest of the demo so soon.

Simply ask then, what does the verb "to increment" mean?

To increase or gain. 

If you're still stuck, the synonym you're looking for is a number.