Question

Which of these quantities represents an infinite set?
the number of grains of sand in the world
the number of ways to walk from your house to the closest store
the number of people who pass through the Panama Canal each day
the number of cars that will use Interstate 10 tomorrow

i picked the number of grains in the world but got it wrong

Answer 1

the number of people who pass through the Panama Canal each day

it has the each day, and days never end.

:-)

Answer 2

The number of ways to walk from your house to the closest store is infinite (since you can walk anywhere in the world, and even slight changes are technically different).

Answer 3

even it is the whole worl ot will still end,
but the days i think at the end of the world,

:))))

Answer 4

i still don't get it how can someone count the number of sand grains though?

Answer 5

"the number of grains of sand in the world" cannot be infinite, since there are not an infinite number of particles in the universe, and grains of sand are a subset of this.

"the number of people who pass through the Panama Canal each day" is finite, and is capped at the number of people in the world (7 billion, big but not infinite).

"the number of cars that will use Interstate 10 tomorrow" is finite, since cars are manufactured, they must have a finite number.

Answer 6

because even it is hard you can still count it because it is limited,

Answer 7

With the walking, you can move 1 yoctometre (10\(^{-24}\)) metres to the left at any point in your journey, and it will still be a different route.

Answer 8

ok good point

Answer 9

but wouldn't it eventually be a set amount of different ways to walk?

Answer 10

No, space can be infinitely divided, there's no smallest amount of variation you can make in your route.

Answer 11

they didn't set any amout so you can do whatever you want.

Answer 12

ok you was right i turned it in and said 100% thank you still don't quiet get it though

Answer 13

In a practical sense it's not infinite, but in a technical, and theoretical sense, it is infinite.

Answer 14

Think of the smallest variation you could possibly make to your walking route. There will always be a smaller variation :)

Answer 15

alright haha never thought about it like that

Answer 16

i agree with dalvoron - the walk is the only one thats infinite