I don’t know how these simple calculators work.

[peterrowlett@mathstodon.xyz]

I don’t know how these simple calculators work. My son has noticed if he repeatedly square roots, say, 0.7734 it converges on 0.9999998 but then just sits there. Why does it think √0.9999998=0.9999998?

[oscarcunningham@mathstodon.xyz]

@peterrowlett Suppose the largest representable number below 1 is 1 - ε. Then the Taylor expansion of √(1 - ε) is 1 - ε/2 - ε²/8 + …, which is closer to 1 - ε than it is to 1. So it's correctly rounding the correct result.