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
∞ is alt-5 or opt-5 on a mac.
It seems like you have a perfectly good explanation in your hands already: ∞ isn’t a number, and operations like addition, multiplication, and exponentiation require two numbers as inputs, and give back a third (not necessarily different) number as a result.
Treating ∞ as a number is sloppy practice: you should always be trying to write lim (x » ∞) of 1^x instead of 1^∞. (» is not the right glyph, but I can’t find right-arrow on my keyboard)
Meanwhile, lim (x » ∞) of 1^x is perfectly well defined: it’s 1. If you have a sequence of real numbers that tends toward infinity, for any difference ∂ you care to name (edit: ∂ > 0), there is a number *n* such that, after *n* elements of the sequence, the difference between 1^a (where *a* is from your sequence) and 1 is less than ∂. Specifically, that distance is zero, because 1 raised to any real number gives 1.
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