One of the major complaints Wildberger makes is that the contemporary maths student is tricked into believing the current infinitist dogma because the details and foundations are hidden from him. They say that worrying about foundations is the job of a logician. Here take these unjustified axioms and go work with them. Real numbers are usually not "constructed", and even when they are, their properties are never proved to the undergraduate. What's more, what constitutes a proof is never explained. Often universities allow students to assume "knowledge" from high school even though the way the student learned in high school doesn't meet the standards of rigor in the university, making the whole thing quite shaky and disconnected.
So my question is this: is there a book or a resource that explains modern mathematics from the beginning (meaning from the foundations) and without assuming any sneaky outside knowledge?
Is Bourbaki the only project similar to that?