I’m also British, for what it’s worth. Of course anyone can study the foundations of calculus. The question is whether it’s reasonable for someone to choose not

I’m also British, for what it’s worth. Of course anyone can study the foundations of calculus. The question is whether it’s reasonable for someone to choose not to and trust that it works. I think it surely is reasonable for someone to do so, unless they have a particular need for a deep understanding of calculus. You always have to stop somewhere. Any given one of your assumptions may be verifiable in principle, but you won’t have the time and wherewithal to verify all of them. Science as it’s actually practiced is a huge pyramid of trust.