Question

1There are infinitely many stations on a train route. Sup-

nOse that the train stops at the first station and suppose

that if the train stops at a station, then it stops at the next

station. Show that the train stops at all stations.​

Answer 1

Answer:

to prove the above result Use the method of induction

The statement is true because the train stops at the first station.

For the inductive hypothesis assume that is true.

That is, the train stops at thestation then it stops at the station since a train stops at one station then it stops at the next station too.

Therefore, the statementis true.

Hence, by the principle of mathematical induction, is true for all for all positive integers

Answer 2

Given: there are infinitely many stations, the train stops at the first station

To prove: Train stops at all the stations

Proof:

The train stops at the first station (given)

Assuming it is true,

The train will stop at the next station.

Since, if the train stops at one station, it will stop at the next station too.

Therefore, this statement is true.

Hence,

Using Principal of Mathematical Induction,

This is true for all the infinite stations.