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Theorems about Continuous Functions Part 1 - The Intermediate Value Theorem (with Fabian Gabel)
In the first part of a mini-series about properties of continuous functions we discuss the intermediate value theorem. We shall conclude that intervals are preserved under continuous mappings and provide another proof of the discontinuity of functions jumping from 0 to 1. Proving the intermediate value theorem, we have the occasion to revisit an argument we used to prove that the reals are uncountable.
Picture: Steven Baltakatei Sandoval, CC BY-SA 4.0, via Wikimedia Commons
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By profmoppiIn the first part of a mini-series about properties of continuous functions we discuss the intermediate value theorem. We shall conclude that intervals are preserved under continuous mappings and provide another proof of the discontinuity of functions jumping from 0 to 1. Proving the intermediate value theorem, we have the occasion to revisit an argument we used to prove that the reals are uncountable.
Picture: Steven Baltakatei Sandoval, CC BY-SA 4.0, via Wikimedia Commons