Confusion Understanding Faraday's Law of Electromagnetic Induction

What happens if time becomes a negative number?

" ... voltage (E) equals flux (Φ)*Number of turn / Δt."

Think you missed out an important word (and symbol). Try:

" ... voltage (E) equals flux change (ΔΦ)*Number of turns / Δt."

How much will the flux change in zero time?

You don't quite have it right, see here. It is the change in magnetic flux divided by the change in time. It simply means that the faster you change the magnetic flux, the more induced voltage you get.

Actually, division by zero is undefined. not infinity.

http://en.wikipedia.org/wiki/Division_by_zero

While it is true in the example they give (y=1/x), that as x approaches 0, that y approaches infinity, that is different from x=0 (x at 0).

E= N* (dΦ/dt) which means that E is proportional to number of turns and to the "time derivative" of the flux. The last means the "rate of flux change versus time". It is NOT a simple division as you assume in your question. In fact you wrote the equation in a way which shows that you did not understand what it means.

along with the rule, the condition was dt not = zero. As you very much understand, mathematically, then it would be infinte. What we are taught is with finite nos.! All science theories are based on hypothesis that the ultimate result is not infinite. Our Engineering Mathematics stops here.

I dare suggest to read what I wrote. The derivative can only in a singular point tend to infinite and this because of the function one will derive. A derivative is what is called a "limit" and NOT a DIVISION. Basic differential computing.

Have you ever heard of the Calculus?

When time = 0 - voltage = 0 - as does most everything else!

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Where did the zero come from? Apples times oranges always equals lemons.