Floating-Point Representation Limits¶

Floating-point numbers are finite approximations of infinite real numbers; representation gaps, rounding errors, and precision loss are mathematically inevitable - not implementation bugs.

Tension Addressed¶

Precision vs. Performance

Recognizable As¶

0.1 + 0.2 != 0.3, accumulated errors in long computations, comparison with epsilon tolerance, special values (NaN, infinity), loss of significance.

Canonical Sources¶

Goldberg, "What Every Computer Scientist Should Know About Floating-Point Arithmetic" (1991); Kahan, IEEE 754 standard work

Transfers To¶

Financial systems (why they use decimal), scientific computing, graphics, game physics, machine learning numerical stability

This is not a bug - it's a mathematical constraint. Infinite real numbers cannot be represented in finite bits. Understanding this prevents bugs and guides representation choices.