Sonya states that the distance along a line should be a defined concept because she can find such a distance. She measures the distance between points on the line, A and B, to be 3 inches. Darren claims that she did not find the distance along the line. Which student is correct? Explain.

Question

kittybasil · Answer

Darren is the one who is correct because a line is infinite (has no beginning/end); this is compared to a line segment, which is between two points (and what Sonya actually measured) and finite (has a beginning/end). We must also realize that Sonya's measurement unit, inches, requires us to use the concept of distance to properly define it. But you can't define a line because it's not measurable like that - can you measure infinity? No, which is why Sonya is not right.