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Is \(0^0=1\) and can be applied everywhere in mathematics?

Note by Aditya Parson
4 years, 3 months ago

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exact zero raise to the power exact zero is NOT DEFINED. Ashutosh Mittal · 4 years, 3 months ago

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Read this funny yet informative article http://www.askamathematician.com/2010/12/q-what-does-00-zero-raised-to-the-zeroth-power-equal-why-do-mathematicians-and-high-school-teachers-disagree/ Saurabh Dubey · 4 years, 3 months ago

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Watch this video Micah Wood · 4 years, 3 months ago

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http://www.wolframalpha.com/input/?i=lim+x+is+approaching+to+0+x%5Ex Tan Wei Sheng · 4 years, 3 months ago

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In calculus and other branches of mathematical analysis, an indeterminate form is an algebraic expression obtained in the context of limits. Limits involving algebraic operations are often performed by replacing subexpressions by their limits; if the expression obtained after this substitution does not give enough information to determine the original limit, it is known as an indeterminate form. The indeterminate forms include 0^0, 0/0, 1^∞, ∞−∞,∞/∞, 0 × ∞, and ∞/0.........so it's also a indeterminate form you have given.... Raja Metronetizen · 4 years, 3 months ago

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0^0 = 0^(m-m) = 0^(m) . 0^(-m) .... now as, 0^(-m) = 1 / 0 which is undefined... so 0^0 = undefined .....well first I tried to prove it like this but then I found that it wasn't a good proof as it had contradictions . :( Zubayet Zico · 4 years, 3 months ago

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it is indeterminate form in chapter limits.... Riya Gupta · 4 years, 3 months ago

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@Riya Gupta but mathematicians prove through limits that it it comes to 1? Aditya Parson · 4 years, 3 months ago

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@Aditya Parson ok......can u xplain me how? Riya Gupta · 4 years, 3 months ago

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@Riya Gupta read the article posted by Saurabh. Aditya Parson · 4 years, 3 months ago

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@Aditya Parson ok thanks....i'll do that... Riya Gupta · 4 years, 3 months ago

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@Riya Gupta limits tell us that n/0 = inf but we know that n/0 is undefined Djordje Marjanovic · 4 years, 3 months ago

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well someone can give me the clear proof of any number raised to 0 is 1. Diksha Verma · 4 years, 3 months ago

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yes we can prove it by log theorem? take log and calculate. Attain k Gupta · 4 years, 3 months ago

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0^0=0/0-------------not defined Sreehari Vp · 4 years, 3 months ago

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look at this.

4^2 = 16

4^1 = 4

4^0 = 1

why 4^0 = 1?

easy to proof. imagine that the exponent is absolutely like an element of carbon molecule. exponent is like a box that contain something, copy the box and paste then imagine that they will combine and has more energy, it will be two thing that are same like x*x in mathematic.

how about x^0?

so easy. it means that there are no element, like an empty box. because the box still present in universe, it mean there must be a symbol to represent it, that is the 1 or one. Yulianto Indra Setiawan · 4 years, 3 months ago

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If 0^0=1 what's the proof and if 0^0= undefined what's the proof ??? Zubayet Zico · 4 years, 3 months ago

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really nice question....... i think so it is undefined. Diksha Verma · 4 years, 3 months ago

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@Diksha Verma I agree with that. You can easily prove that it is an indeterminate form in mathematics, Aditya Parson · 4 years, 3 months ago

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@Aditya Parson in laws of exponent they never mention that base a is not equal to 0 Diksha Verma · 4 years, 3 months ago

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undefined. bt nt equal 2 1. Shubham Malik · 4 years, 3 months ago

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The way I was taught, even though 0^0 is indeterminate, mathematicians will consider it to be 1. Kenneth Chan · 4 years, 3 months ago

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@Kenneth Chan considering is different thing...sometimes in physics also we consider that 1/0 = infinity...but that is wrong.. 0^0 is undefined Arushit Mudgal · 4 years, 3 months ago

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it should be zero.. Diksha Verma · 4 years, 3 months ago

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@Diksha Verma But many take it to be 1. Aditya Parson · 4 years, 3 months ago

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@Aditya Parson LIke google! https://www.google.com/search?q=0^0 Kenneth Chan · 4 years, 3 months ago

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@Kenneth Chan Yes. Aditya Parson · 4 years, 3 months ago

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@Aditya Parson only google calculator is showing 1! but other scientific calculators finds math error. Diksha Verma · 4 years, 3 months ago

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@Diksha Verma I know that. Aditya Parson · 4 years, 3 months ago

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@Aditya Parson 0^0 is neither 1 nor indeterminate, it is undefined... there is a difference between indeterminate and undefined. e.g. app.0/app.0 is indeterminate where as 0/0 is undefined similarly, 0^0 is undefined as 0^0 = e^(0log0) where log 0 is undefined, but (app. 0)^app.0 is indeterminate whose value is 1...if both functions which are approaching 0 used in (app0)^app0 are the same. if both functions are x. lim (x app0) x^x can be found by equating it to e^xlogx where if xapp. 0 xlogx approaches 0[this can be found by using LH rule] and hence x^x approaches 1(as e^0 = 1) Jatin Yadav · 4 years, 3 months ago

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@Aditya Parson Just a consideration Arushit Mudgal · 4 years, 3 months ago

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