invertible

Dual numbers use nilpotent infinitesimals (which are not invertible), while non-standard (Robinson) infinitesimals are not nilpotent and are invertible.

Isomorphic means there exists an 'isomorphism' or an invertible function between two things that aren't the same.

You can't connect a matrix of positive determinant with one of negative determinant without going through non-invertible matrices.

The space of invertible linear transformations is actually a Riemannian manifold, and in particular a Lie group.

The reason mutation doesn't seem to be prevalent, is because a lot of operations that are studied are invertible.

Thus, g(x) is a unit[2] (ie invertible), and every nonzero element of F[[x]] is a unit multiple of a power of x.

That's why the Bitcoin devs are working on invertible Bloom lookup tables.

For instance, diagonalizability is not necessary for invertibility---shearing transformations can be invertible.

The set of invertible linear transformations is also not connected.

This issue is being addressed via invertible bloom lookup tables.

Inb4 'merkle trees', 'invertible bloom filters', 'something something moore's law', 'the market will sort it out', 'side chains', etc.

Of course, not all function is invertible.

I think parent is asking more about the added value of "invertible" bloom filters.

But there's so much more to the "invertible" paradigm.

Any quasi-random permutation will work, I just figure "let's take the ones that are only a couple fixed lines of code." The nice thing about these permutations, too, is that they're invertible: someone gives you a name, you convert it to a number, you pass it back through this, and you get map/geodesic coordinates.

Invertible bloom filters are an elegant and simple solution to one of the main limits to bitcoin scalability: the time it takes to propagate solved blocks.