1 ^ ∞, It's Not What You Think

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In this video, we explore the concept of 1 raised to the power of infinity. At first glance, it may seem like the answer should be 1, but as we dive deeper into the topic, we quickly realize that it's not that simple. We discuss the limitations of using limits to try and determine the value of 1^infinity and how the traditional definition of exponentiation doesn't allow for infinity to be used as an exponent. We also explore an alternative approach, using logarithms, to try and determine the value of 1^infinity. We show how logarithms allow us to rewrite exponential expressions as a power of the base, and how in this case, 1^infinity can be rewritten as log(1^infinity) = infinity * log(1) = infinity * 0, which is undefined.

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