Infinity Question

Question

This question comes from timed a JavaScript Challenge. The question is:
What is the output of the code?
let a = 1;
let b = Infinity;
let c = 0;
let x = (a/b) == c;
let y = (a/c) == b;
const z = x == y;
console.log(z);

The output is true.

Is this because 1/Infinity is 0 and 1/0 is also 0?

Thank you for helping! ❤️

Answer 1

1/Infinity is 0, so x contains `true`.
1/0 is Infinity, so y contains `true`.
The output is true because `true == true`!

Answer 2

[definitely meta] Mostly to help you think about questions playing with Infinity (and why 1/0 and 1/-0 are different).

1/0 describes what you're approaching on the way to 0 from "above" (i.e., the positive side)

Visualization:
Place 1/x in a formula line here:
https://code.sololearn.com/WWE2g9B1nka6/?ref=app

Then follow the graph towards 0...as x approaches:
0 from the right, the graph blows up towards infinity (1/0.00000000001 is a very positive number)
-0 from the left, the graph plummets down towards -infinity (1/-0.000000001 is a very negative number)

In Javascript, approaching 0 from either side produces two different results:
1/Math.round(0.1) = Infinity // rounds to 0
1/Math.round(-0.1) = -Infinity // rounds to -0

Mostly just FYI but it may help explain why Infinity shows up there.
~ (Signed 0's are used for tracking state in some langs/maths)

Answer 3

Ohhhh! 1/0 is Infinity.

Ok, thanks!

Answer 4

Thanks, Schafer 😃 your calculator is mind blowing!

Answer 5

Ah, I'm only linking into a public API because it has extra abilities like: extract the formulas / control it programmatically / creating my own webpages...
...but the majority of the code is Desmos'. The Android app is pretty good for the general use case :)

Answer 6

Kirk Schafer P.S. My last name is also "Shafer" but I just realized you have no way of knowing that.