Cardinality of Line Segment & Half Circumference: Bijection Established

[MikeDietrich]

Homework Statement
Do the following have the same cardinality? If so, establish a bijection and if not explain why.

A line segment of 4 units and half of a circumference of radius 1 (including both endpoints).


The attempt at a solution

So my thought is that if I manipulate the shape of these two figures I have two circles of different sizes and if I place one inside the other then I can show they have the SAME cardinality by radiating lines from the center of each to the edge of the large circle.

First of all, I am not even sure if this is appropriate/accurate to do and then I do not know how to establish a bijection (aside the picture).

Any thoughts or suggestions? Thank you in advance!

 

[tiny-tim]

Hi Mike!

You're both being too analytical and not reading the question carefully enough …

Do the following have the same cardinality? If so, establish a bijection and if not explain why.

The question does not ask you to explain why, in the case that they do have the same cardinality …

it only asks for a bijection (which of course is a complete explanation in itself anyway).

So just write out an equation. ​