To end this discussion,I post a reply I got from another expert. Thanks all for the replies. Finally brushed-up on Ohm's law.
"Take circuit below with a resistor R and a REAL power supply. An ideal power supply has no internal resistance, but the real ones have always some internal resistance R1. The circuit looks like this
|-----R--o--R1---IDEAL_SUPPLY--o--|
|_________________________________|
Think that R1 and IDEAL_SUPPLY are inside the same box, which is the real-world power supply (e.g. battery). in the circuit above "o" marks the connection points.
Since the power supply's internal resistance and the resistor are in series, the total resistance in the circuit is R1 + R. The current I is by Ohm's law equal to V/(R1 + R) . For that reason, even if R=0, I is still = V/(R1+R) = V/R1.
That is why a real power supply can never give infinite current.
With regard to the voltage, it is an innate characteristic of the power supply. The voltage you measure across the resistor is known as the "voltage drop" in the resistor and is equal to I * R (where I is the current flowing through the circuit above). If R is zero (short circuit), then the voltage is equal to I * 0 = 0. The value of I flowing through that short circuit is still determined like above.
In any case, don't go too deep in this unless you really want to learn physics (and have the time to do so -- it's a different field of study and you can't approach it from the pure math point of view. The real world is always more complicated than ideal formulas)".