Let's talk analysis: Can we do calculus in the rationals?

We haven't been able to completely characterize the rational numbers but we have an idea of what they are. Can we do calculus only using the rational numbers? Why do we need to come up with real numbers? and what are the real numbers anyways?
Join us as we explore this questions!
The following videos would be a great place to prepare for this stream!
• Why the rationals are ...
• Unveiling the Gaps: Wh...