Im studying calculus this year and one of the lectures included undefined values (*forbidden and unwanted* not my words btw). These included:
1. 0/0
2. oo – oo
3. oo/oo
4. 0*oo
5. 0^0
6. oo^0
7. 1^oo
All of these are extremely weird to me and I don’t really understand them, but the one that strikes me the most is the last one. As a former math competitor and regarded as “gifted” in math, I feel stupid not being able to comprehend this, but most importantly it shatters my belief that math can explain everything and that is has all the answers.
I don’t see infinity as a really big number, I understand it as a concept, and what confuses me the most is seeing infinity treated as number. 1^oo for me doesn’t make any sense. It seems mathematically absurd. Infinity isn’t number, it’s a quantity that can’t be measured. And if it is treated as a number shouldn’t 1^oo = 1?
How come these are “undefined”? Someone please answer, Im losing my mind over this. All explanations are welcome, shallow or deep.
edit: to clarify oo = infinity
In: Mathematics
There are 2 reasons that these formulas are forbidden and unwanted:
1. Infinity and zero have many different definitions. This is especially important with Taylor series, where you can have an infinite sum of numbers go either to a finite or infinite number depending on the series.
2. When a solution goes to infinity or zero, it’s often a trivial case to a real world problem that has multiple possible answers. It’s like saying you’re going to solve both sides of an equation my just multiplying them both by zero. Yes it works under the rules of math, but it’s useless.
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