The language just gives you the direct comparison.
If you know numerics, then you can come up with the correct value for epsilon. But that is hard work. There are various things that the language could do for you, like use a dynamic amount of precision, or interval arithmetic where the error bounds are saved—but! Most of the time people just want the answer faster and with less memory used, which is what you get with bare floats. The people who make it their job to care about numerical accuracy can do it better than the language runtime would anyway.
Most of the problems are more easily solvable at a higher level anyway. Like, imagine Clippy saying to you, “It looks like you’re inverting a matrix. Are you sure that’s a good idea?”
If you know numerics, then you can come up with the correct value for epsilon. But that is hard work. There are various things that the language could do for you, like use a dynamic amount of precision, or interval arithmetic where the error bounds are saved—but! Most of the time people just want the answer faster and with less memory used, which is what you get with bare floats. The people who make it their job to care about numerical accuracy can do it better than the language runtime would anyway.
Most of the problems are more easily solvable at a higher level anyway. Like, imagine Clippy saying to you, “It looks like you’re inverting a matrix. Are you sure that’s a good idea?”