Harish Kumar

From what I have been reading there is a trade-off between speed(rpm) and torque, and how does an electric motor, starting from zero rpm able to produce the necessary torque to turn the wheels which are standing still. Wouldn't even the electric motor need to be running at certain rpm to produce the torque required to turn the wheels from standstill?

I wish to thank all the guys here for clarifying my doubt. Thank you once again!

I would like to know the need for Gear Boxes. Can't we just couple the car engine to the wheels directly without using gears? If we change the RPM of the engine by controlling fuel injected, the speed of the car is automatically controlled. Why do we need gears which cause loss of efficiency while transmitting power due to friction, etc. Likewise, cant we connect the steam turbine shaft directly to the screws of the submarine, instead of routing it through a gear box? Aren't gears bringing down the efficiency of the engines which consume a lot of power? Can anybody clarify?

Thank you very much uncool. And sorry for the delayed response. I was revisiting my college maths and I was tied up with too much work at the workplace. I appreciate your clarification very much.

Nobody in the mathematics department?

This is an example from I N Herstein's Topics in Algebra: Let S be a set of all Integers. Given a,b belongs to S, define a~b if a-b is an even integer. He goes on to say that in this case, the equivalence class of A consists of all the integers of the form a+2m, where m=0,+-1,+-2,+3...; and in this example there are only two distinct equivalence classes,namely cl(0) and cl(1). Clearly cl(0) and cl(2) will have many elements in common. So is not the "mutually disjoint" condition broken in this case, since the intersection of Sets cl(0) and cl(2) is not a null set? Can you please clarify?

But with today's computing power, is it really necessary to convert non-linear equations to linear equations? May be you get results quickly, but you lose the accuracy you will get if you wait for a few hours or a few days!

But then if we create a relation, a~b, a,b belong to Integers, where every member is divisible by 2, aren't those members also present in the relation "divisible by four" ? So how come we say they are mutually disjoint?

I am not able to understand clearly the concept of equivalence classes. Is it mandatory that for a particular equivalence relation in Set A, all the equivalence classes are either mutually disjoint or equal? Or are they mutually disjoint for all possible E-relations for a set A(or only on specific E-relation?)? Secondly, In the equivalence relation: Let S be the set of all integers and let n > 1 be a fixed integer. Define for a,b belonging to S, a~b, if a-b is a multiple of n. How is it, in the case above, the equivalence class of a consists of all integers of the form a + kn, where k=0,1,-1,2,-2,3,-3,...; there are n distinct equivalence classes, namely cl(0), cl(1),...cl(n-1), when clearly cl(2), cl(4) have elements in common?