an integral domain is a commutative ring with no zero divisors
First suppose the multiplicative identity 1 has finite order n 0. So n*1 0 Then for any element x, nx (n*1)x 0*x 0 So every element has additive order less than or equal to n. Now suppose we have a nonzero element x with additive order m n. Then mx 0. But m is an element of the integral domain and x is nonzero, so since there are no nonzero zero divisors, m 0 (in the integral domain) i.e. m*1 0 So the additive order of 1 must be less than or equal to m, which contradicts that m n. Therefore every nonzero element has additive order n. Finally, if 1 has infinite additive order then we show that all nonzero elements have infinite additive order. For suppose x is a nonzero element with finite additive order. Then mx 0 for some m 0. But again, since there are no nonzero zero divisors and x is nonzero, we must conclude that m 0 (in the integral domain) i.e. m*1 0. So 1 has finite additive order, contradiction.
The brakes will still work just not as good and you will have to use a lot of force on the pedal.
try this just turn ur ignition key on to unlock the steering wheel do not start the car .now try turning the wheel all the way to the right and than to the left.this is going to be how hard it will be for you to brake(stop)your car without the booster.God help you if you need to brake for an emergency cuz it aint going to happen.i know this cuz i drove a car with the brake booster not working and it was a terrifying event.good luck
