Preposition

1. Against; next to; near; towards.

   Go up to the counter and ask.

2. Doing; involved in.

   What are you up to these days?

3. Able; willing.

   Are you up to lifting something that heavy?

4. As much as; no more than.

   You can make up to five copies.

5. The option or decision of.

   It’s up to you whether to get the blue one or the red one.

6. Considering all members of an equivalence class the same.

   There’s only one rooted tree with two leaves, up to ordering.