The dual numbers exist just as surely as the real numbers and have been used well over 100 years https://en.m.wikipedia.org/wiki/Dual_number https://en.m.wikip

The dual numbers exist just as surely as the real numbers and have been used well over 100 years https://en.m.wikipedia.org/wiki/Dual_number https://en.m.wikipedia.org/wiki/Dual_number Pytorch has had them for many years. https://pytorch.org/docs/stable/generated/torch.autograd.forward_ad.make_dual.html https://pytorch.org/docs/stable/generated/torch.autograd.for... JAX implements them and uses them exactly as stated in this thread. https://github.com/google/jax/discussions/10157#discussioncomment-2513008 https://github.com/google/jax/discussions/10157#discussionco... Many other frameworks use them also, for many reasons. As you so eloquently stated, "you shouldn't be proclaiming things you don't actually know on a public forum," and doubly so when your claimed "corrections" are so demonstrably and totally incorrect.