A lot of people think math is never ambiguous which is false.
0⁰ is a perfect example of what ambiguity looks like in mathematics. 👇🧵
0⁰ is a perfect example of what ambiguity looks like in mathematics. 👇🧵
Let me give some intuition for why the situation is ambiguous.
On the one hand, 0³=0. 0²=0. 0¹=0. So logically, one might conclude that 0⁰=0.
On the other hand, 3⁰=1. 2⁰=1. 1⁰=1. So logically, one might expect 0⁰=1.
On the one hand, 0³=0. 0²=0. 0¹=0. So logically, one might conclude that 0⁰=0.
On the other hand, 3⁰=1. 2⁰=1. 1⁰=1. So logically, one might expect 0⁰=1.
Sometimes people will say 0⁰ is "indeterminate" meaning "we don't know what to do here so it's best to avoid it completely".
It's the mathematical equivalent of raising the white flag and declaring surrender.
This is also how we handle dividing by zero.
It's the mathematical equivalent of raising the white flag and declaring surrender.
This is also how we handle dividing by zero.
Unfortunately (or fortunately), having a value for 0⁰ is really helpful in a lot cases.
Many find it much too convenient to just completely avoid it.
Many find it much too convenient to just completely avoid it.
My own personal opinion is that arguing from lots of different special cases, 0⁰=1 seems to be the most reasonable solution, but the "right" way to handle 0⁰ generally depends on the application and the context.
To summarize, there are three broad strategies for dealing with ambiguity in mathematical calculations:
1. Avoid the problematic calculation completely
2. Choose a value that works in most but not all cases
3. Use whatever works for you in the current situation
1. Avoid the problematic calculation completely
2. Choose a value that works in most but not all cases
3. Use whatever works for you in the current situation
Reference: the wikipedia article on 0⁰ is very good if you want to read more about it. en.wikipedia.org
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