[Math] What do these symbols mean in equations 4 and 5 on this page

algebra-precalculusnotation

I'm looking at an old math textbook on the Internet Archive. On
page 17 of this pdf at the bottom it has 2 formulas.

One has what looks like an apostrophe and the other has a dot (like a decimal but floating).

Question: Can someone explain what these symbols mean?

Best Answer

It's just a comma and a period — mathematical text is still text.

Presumably you wouldn't be as surprised if you saw

... it follows that: $I_0=\dfrac{Pdi}{360}$, and $I_e=\dfrac{Pdi}{365}$.

but in order to emphasize and label the equations, we put them on their own line. We nevertheless should keep the punctuation. Take a look at this MathOverflow thread.

Related Solutions

[Math] Notation Question: What does $\vdash$ mean in logic

Let $S$ be a set of (logical) formulae and $\psi$ be a formula. Then $S \vdash \psi$ means that $\psi$ can be derived from the formulae in $S$. Intuitively, $S$ is a list of assumptions, and $S \vdash \psi$ if we can prove $\psi$ from the assumptions in $S$.

$\vdash \psi$ is shorthand for $\varnothing \vdash \psi$. That is, $\psi$ can be derived with no assumptions, so that in some sense, $\psi$ is 'true').

More precisely, systems of logic consist of certain axioms and rules of inference (one such rule being "from $\phi$ and $\phi \to \psi$ we can infer $\psi$"). What it means for $\psi$ to be 'derivable' from a set $S$ of formulae is that in a finite number of steps you can work with (i) the formulae in $S$, (ii) the axioms of your logical system, and (iii) the rules of inference, and end up with $\psi$.

In particular, if $\vdash \psi$ then $\psi$ can be derived solely from the axioms by using the rules of inference in your logical system.

[Math] What does a dot after a number mean

Wolfram Alpha is trying to tell you that it is not exactly $2$, but very close to $2$. Try using fractions to gain an exact answer:

-2/3 (x-1) (x-1/2) (x+1/2)+ 1/6 (x-1) (x+1) (x+1/2)+ 1/2 (x-1) (x-1/2) (x+1)

Which is $\frac{x^2 - x}{2}$.

Best Answer

Related Solutions

[Math] Notation Question: What does $\vdash$ mean in logic

[Math] What does a dot after a number mean

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