Equivalence relation in singular homology I'm currently reading Rotman's Introduction to algebraic topology, and I'm struggling to understand what singular homology is.
The definition of a singular simplex isn't clear to me. If a singular simplex is any continuous map from the standard n simplex, then there are uncountably many of them (except for some special spaces). The point that I don't get is how all of those simplexes "cancel" each other in the homology group. I read about an equivalence relation that takes care of it but I didn't understand.
Thanks in advance!

You are sort of correct. Singular homology is not really "computable".
However, one can show that it is naturally isomorphic to (semi)simplicial homology, CW homology, etc, and others are somewhat computable, giving you the results.
Simplexes do not trivially cancel as what you expected.
