Please bear with me with this as I am by no means an expert.

If there are only to be a set amount of Bitcoins produced to stop inflation, then presumably instead of mining more bitcoins, people will start using up all of the 8 decimals i.e. breaking up bitcoins into ever smaller chunks and renaming them

This seems to me to have the same result as inflation, does it matter if we call 0.001BTC a bitcoin or 1BTC a bitcoin, its only a name? Is there a way so safegurd against this or is it even a big deal?

And if we were to break down all bitcoins all the way, how would the total amount of units compare to the total units of say the dollar or euro?

 
Intrigued and bewildered.