You are watching: What does the asterisk mean in math

In calculus, as soon as studying sigma notation, particularly with Riemann sums, you regularly see something choose this:

$$A = \\sum_k=1^n f(\\colorredc_k^\\colorred*)\\Delta x$$

I know that in the certain case that Riemann sums, it way that you are to select any type of $c_k$ in the term $

My question: what is the surname for (or exactly how to girlfriend pronounce) the $\\colorredc^\\colorred*$ term?

More generally, what do you call a change or hatchet that has actually an asterisk above it like, that? And, what is the tennis2007.orgematic an interpretation of the asterisk, in a general sense?

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edited Dec 4 \"15 at 23:08

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tommytwoeyestommytwoeyes

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I would certainly pronounce it \"c-k-star\". The meaning is simply that these are new values supplied to approximate the previous values, so like the $c_1, \\ldots, c_n$ define regions of the number line, and $c_k^*$ is not one of these values, yet it is supplied to essentially approximate $c_k$ (being between $c_k-1$ and $c_k$). There are several means to pick this value, one of two people a left ($c_k^* = c_k-1$) or best ($c_k^* = c_k$) endpoint of the interval, or a mid point ($c_k^* = \\fracc_k-1+c_k2$), or yes, really it can be chosen arbitrarily (it will all come the end the same as soon as you take the border over a partition refinement).

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answered Dec 4 \"15 at 23:22

Morgan RodgersMorgan Rodgers

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To price the second component of your question: the asterix has a many of various meanings. Sometimes it is simply a brand-new variable name (like in her example) that should be explained in the text surrounding the formula. Often, this will be some extremum (in case of Riemann sums, the is yet an additional choice).

In various other contexts, the can likewise denote the facility conjugate of a complex number, the adjoint of an operator in a Hilbert space, the double of a linear operator, and really commonly the pullback operator connected to part function. And these are absolutely not every meanings.

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reply Dec 5 \"15 at 3:48

Eike SchulteEike Schulte

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