How can an object (say, car) accelerate from some velocity to another if there is an infinite number of velocities it has to attain first?

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E.g. how can the car accelerate from rest to 5m/s if it first has to be going at 10^(-100) m/s which in turn requires it to have gone through 10^(-1000) m/s, etc.? That is, if a car is going at a speed of 5m/s, doesn’t that mean the magnitude of its speed has gone through all numbers in the interval [0,5], meaning it’s gone through all the numbers in [0,10^(-100000) ], etc.? How can it do that in a finite amount of time?

In: Mathematics

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Anonymous 0 Comments

Because you can’t divide the difference into an infinite number of divisions.  You can always divide again, but every division you do will always result in a finite number of divisions.  At no point no matter how many times you divide will you reach a result of an infinite amount of divisions.  Your ability to divide is limitless but the number of divisions you create are finite.  I e. You can never just “divide one more time” and go from a finite number of divisions to an infinite number of divisions.

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