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FactChecker replied to the thread Undergrad Momentum measurement and uncertainty.Thanks. The terminology is tricky. That is the expected value for a single sample from that distribution. That is not the same as the... -
FactChecker replied to the thread Undergrad Momentum measurement and uncertainty."do statistics" is vague. If you determine the variance of the single random momentum value of a single sample (possibly using a large... -
FactChecker replied to the thread Undergrad Momentum measurement and uncertainty.Do you mean the sample variance of the sample distribution of a large number of measurement data, or the variance of the sample average... -
FactChecker replied to the thread Undergrad Momentum measurement and uncertainty.That sounds wrong or unclear. The average of many may have a very small uncertainty, while the uncertainty (variance/spread) of the... -
FactChecker replied to the thread High School Why simplifying this function generates different outputs for same input?.Correct simplification includes keeping track of where the original function was undefined. -
FactChecker reacted to Dale's post in the thread High School Why simplifying this function generates different outputs for same input? with
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It is forbidden specifically at ##x=2##. Elsewhere it is not forbidden. -
FactChecker reacted to gen x's post in the thread High School Why simplifying this function generates different outputs for same input? with
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This function ##f(x) = \frac{x^2 - 4}{x - 2}## when simplify become ##f(x) = x + 2## . If I enter ##x=2## in the first expression I... -
FactChecker reacted to Mark44's post in the thread High School Why simplifying this function generates different outputs for same input? with
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The two functions are identical except at the point (2, 4). The graph of ##f(x) = \frac{x^2 - 4}{x - 2}## can be thought of as a... -
FactChecker reacted to Mark44's post in the thread High School Why simplifying this function generates different outputs for same input? with
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An important attribute of any function is its domain. The difference between the two functions in the OP is that, because of the... -
FactChecker replied to the thread High School Why simplifying this function generates different outputs for same input?.Good catch! You did very well to check the final answers in the original formula. As you go through a simplification, you should keep... -
FactChecker reacted to kuruman's post in the thread High School Why simplifying this function generates different outputs for same input? with
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Because you cannot "just simplify" unless you specifically exclude ##x=2## at which point, as you have discovered, the function is... -
FactChecker replied to the thread AI AI and translation.I think that's smart on its part. Line by line loses too much context, whereas a new paragraph already indicates some change of subject...