Homotopy Type Theory Sandbox (Rev #11, changes)

Showing changes from revision #10 to #11: Added | Removed | Changed

All The right, real let numbers us are get a the simplified identity model types of type numbers. families Actual working… computation in reality occurs in the rational numbers.

It The doesn’t real work! square You root need does types not indexed actually by exist. type Instead families, which we don’t have here. a partial function on the rationals which is only approximately a square root up to some rational toleranceϵ\epsilon.

ϵ<sqrt ϵ(x) 2x<ϵ-\epsilon \lt \mathrm{sqrt}_\epsilon(x)^2 - x \lt \epsilon

The same goes for analytic functions like the exponential function and the sine and cosine function.

Revision on April 12, 2025 at 01:50:51 by Anonymous?. See the history of this page for a list of all contributions to it.