Practice question · Multiple choice
Zeno argued you can never cross a room: first half the distance, then half the rest, forever. Why does the mathematics of series dissolve the paradox?
Hints
- Write down the time for each half-step. Now add them.
- The number of steps is infinite. Ask whether that forces the total to be.
Show the answer
C. Because the times form a convergent series with a finite total
Why
The steps shrink fast enough that the times sum to a finite number: infinitely many additions with a finite total. Zeno's error was assuming an infinite count of intervals means infinite duration, and the resolution had to wait about two thousand years for the definition of a convergent series.
Practise Number Theory in Action
The app has 5 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
More questions on Number Theory in Action
- The infinite geometric series 1 + 1/2 + 1/4 + 1/8 + … has infinitely many positive terms and sums to exactly…
- Order the stages of the RSA idea.
- An ISBN-10 has digits d1 through d10 and must satisfy: 1 x d1 + 2 x d2 + ... + 10 x d10 is congruent to 0 mod…
- A hash table has 13 slots and uses the hash function 'key mod 13'. Which slot does the key 1000 land in?
- Sort each application by the number-theoretic idea it chiefly rests on.
- Complete the source of RSA's security.
- Select every idea from this unit that RSA depends on.