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If you can devide by zero
Let x be a number very close to 0.let c be a finite non-zero number.xc/x = cx^xc = 1thus0/0 = undefined0^0 = 1
Let x be a number very close to 0.let c be a finite non-zero number.xc/x = cx^xc = 1
Perhaps we don't need to determine the value of these things, what do you think?
My best guess is that there will be no physical system where any measurable parameter is "predicted" to be 0 ^ pi or anything like that.However, if there was, we could measure the parameter and find the result of the calculation.
Is 0 by default positive(+) ?Or is it simply Neutral?
But if We ever had such an imaginary concept of +0 & -0...Then what would come between them?
Why does that last line hold? I'm guessing you meant x^(xc) but perhaps it was (x^x).c Anyway x^(xc) is only approximately 1. Take x = 0.1 and c=10, Then x^(xc) = 0.1Is this an argument based on continuity as x → 0 or something?
Could I also push this question again, please:How (and why) will we determine 0 raised to an irrational power, like 0π or 0e or 0√2 ?Can we prove that 0e = 0 from basic principles?Perhaps we don't need to determine the value of these things, what do you think?
is continuity important in anything
Quote from: Petrochemicals on 08/11/2021 14:08:01If you can devide by zeroQuote from: hamdani yusuf on 02/11/2021 15:13:17Let x be a number very close to 0.let c be a finite non-zero number.xc/x = cx^xc = 1thus0/0 = undefined0^0 = 1
Can you multiply by zero, Yx0 is essentially a non acting sum.
Quote from: Petrochemicals on 09/11/2021 04:13:17Can you multiply by zero, Yx0 is essentially a non acting sum.Yes. The result is 0.
Quote from: hamdani yusuf on 09/11/2021 05:59:39Quote from: Petrochemicals on 09/11/2021 04:13:17Can you multiply by zero, Yx0 is essentially a non acting sum.Yes. The result is 0.Is it? In what situation do you actually get such a sum? I know formula can render this sum under a condition, but the sum is discounted. Saying Yx0 is essentially a contradiction, 0xY is not a sum you would see as it would be discounted prior. 273 x 0 is essentially getting half way through a sum and then stopping, leaving it open. Is it undefined?
I meant x^(cx)Try a smaller number for x, say 10-100. The equation applies for both positive and negative value of x, provided that its absolute value is much smaller than absolute value of c. Hence there's no reason to exclude only when x is exactly 0.
We need to distinguish between exact 0 and approximate 0.
(From Eternal student) ....is continuity important in anything?Hamdani Yusuf replied: It simplifies things, which improves efficiency. Efficiency is a universal instrumental goal.
dx in calculus is approximately 0. It doesn't work when it's exactly 0.
Fractional power is easier to understand when it's in polar format, because we can analyze the magnitude and phase angle separately. For exact 0, the angle has no meaning. For approximate 0, when the power is irrational, any angle is elligible, including 0. For simplicity, it's usually chosen as principal value.
We are trying to make the behaviour at x=0 as much like the behaviour for other values of x as we possibly can. Specifically, we are keeping the value of the expression within some small difference of the value of the expression when x is just off 0 and we are confident that we can make this error as small as we want provided we take x close enough to 0.
If you really believed that the value at x=0 is significantly distinguished from values we obtain when x is approximately 0 but not 0, then continuity is certainly not what you're going to have. No matter how close we get to x=0 we should be prepared to accept that the value of the expression could be very different when x is precisely 0.
Don't get me wrong, there's no reason why continuity of these expressions should be important but we do need to ask the following question: Is it reasonable to imply that continuity is important in some situations and some expressions like the x^(xc) argument but then choose to ignore continuity in some other expressions like 0x ? 0x isn't an amazingly complicated expression or some example I have deliberately cooked up to get another limit. It just does look like one of the sensible expressions we might consider when we're trying to determine 00. What reason would there be for specifically ignoring that expression and prioritising continuity in an expression like x^(xc)?