Bicycle Mechanics - confused about wheel and tire sizes

Tire/rim width, specifically.

Example: I'm thinking about building a wheelset with Alex Adventurer rims (700c) with the Michelin Axial Carbon road tires for a commuter/fun ride setup. The rims are 24.5mm in width and the tires are 20, 23, or 25mm. My question is how important is it for these numbers to match up perfectly? Would the 25mm tires work?

I thought 700c and similar types of measurements were for both a specific wheel diameter and rim width.

Anyway, thanks in advance to anyone who can help me out.

It may be possible to make them all work but the 25's are the only ones I would try. They may be too stiff with a rim that wide. You should have narrower rims I think for tires that size. Narrower than the tire, not an exact match.

Tire/rim width, specifically.

Example: I'm thinking about building a wheelset with Alex Adventurer rims (700c) with the Michelin Axial Carbon road tires for a commuter/fun ride setup. The rims are 24.5mm in width and the tires are 20, 23, or 25mm. My question is how important is it for these numbers to match up perfectly? Would the 25mm tires work?

I thought 700c and similar types of measurements were for both a specific wheel diameter and rim width.

Anyway, thanks in advance to anyone who can help me out.The 700c is specific. There is a range of tire widths that can be mounted on any given rim width. Sheldon Brown has the skinny at www.harriscyclery.com in his tire and wheel sizing stuff.

Assuming you gave the outside width, the inside width is 21 mm. This would give a tire width of at least 35 mm according to Sheldon Brown, but a 32 mm would probably be OK, if your frame and forks have enough clearance.

With a rim that wide, I'd certainly be hesitant to put on any tire less than 32mm. 28mm may work, but there is risk that the tire could blow off and you could get a lot more pinch flats.