how much is algebra dependent on analysis?

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Multivariate calculus is dependent on linear algebra. then how much is algebra dependent on analysis? for example, by using the concept of formal derivative, algebra can mimic differential. it seems algebra can develop differential without borrowing any ideas of analysis. is algebra dependent on analysis? because algebra is based on set theory, and set theory is originated from analysis(fourier series)?, how much is algebra dependent on analysis? and there is one more question I want to ask, oneday can algebra mimic everything of analysis?