The use of β=β for assignment in programming languages comes, not directly from mathematics, but indirectly from the use of mathematics in science and engineering. As an example, consider the formula for kinetic energy, commonly written
ππ£Β²
πΎ = βββ
2
Why isn't it written 2K=mvΒ², which expresses the same mathematical equality in a smaller, simpler form? Or any of the other equivalent rearrangements? It's because formulas have a convention, where the LHS is a single term naming the value you want, and the RHS contains the terms for values you have. That is, a formula doesn't just state an equality, it states a method for calculating something. That usage predates programming, and was explicitly copied by early programming languages like For[mula]tran[slator] that were designed for scientific & engineering calculations.
Because I started programming before taking maths at school, I didn't properly appreciate equality for a while.
Sure, algebra was fine, a(x+y)=ax+ay can go either way; but not ratios and other relationships.
What helped me was was geometry, where you can see it's just a relationship. All the components move together; one part isn't priviledged as the result.
e.g. you enlarge a circle.
It doesn't make sense to ask whether the radius made the circumference bigger, or the circumference made the radius bigger.
I remember starting with QBasic when I was around 7 or 8 years old, and I quickly got an idea β just put in the equations from math homework to find out the answer! Fighting through the error messages without English and trying to wrap my mind around the basic concepts of procedural programming was a world of pain.
Nice. I had fun in some junior high math competitions in part by writing TI BASIC programs on my calculator to brute force hard problems while I did the easy ones. Eventually they stopped allowing calculators altogether and focused on cheap memorized tricks instead of generalized problem solving.
I didn't downvote, but the reason is likely because your comment is off-topic. The parents are talking about experiences un-learning one-sided equality that they picked up programming before learning algebra; your comment is about programming a T-83 to help with schoolwork.
I believe it comes directly from conventional math exposition. In a general form itβs about emphasis.
βThe change of subject from βThe dog bit the boyβ to βthe boy was bitten by the dogβ is similar to the change of subject in a formula, as for example β¦ In each case, the two sentences state the same relationship, but with different emphasis.β [1]
While this reasoning may be common, I don't think it's to anyone's benefit. Talking about "the" formula for kinetic energy seems nonsensical, when there are so many ways to state that relationship. Another option is p^2=mK.
But there is a good reason to write it as K=mv^2/2 which has nothing to do with specifying a computation. It is the result of symbolic integration of p=mv with respect to v.
And, perhaps more intuitively, its the second integral of m with respect to v. This pattern also shows up in eg A = β«β«ΟβrΒ² for the area of a circle.
If the expression is supposed to be the definition and not just a derived equality, at least Mathematicians (and some Physicists) would use := instead, just as Niklaus Wirth tried to establish with Pascal.
There are many strange symbols in math already that can be difficult to type without something like LaTeX. I feel like something pronounceable is usually better unless you have a sufficiently general idea.
> "why haven't scientists come up with more symbols yet?"
Take an advanced math test and try to type it out. Being in no sense historically limited by typewriters/keyboards, you might be surprised at the complexity of the symbols.
> It's because formulas have a convention, where the LHS is a single term naming the value you want, and the RHS contains the terms for values you have.
I've seen that, too, but there is usually a reason for writing it in that form. The most common would be that you have a different equation with 2K in it, and so you want to make variable substitution simpler. Alternatively, if you are reading older papers, typesetting inline equations that don't fit in a single line was painful. For that reason, a formula might be rearranged to avoid needing any fractions.
While I donβt think the terminology is explicitly standardized, I think most people in the relevant fields would call that statement of the ideal gas law an equation but not a formula, the latter being a special case of the former.
Can you find any reference to the idea gas law as a βformula?β As far as I can tell, equations without a single variable on the left side are referred to as simply equations, while solutions of such equations in terms of one variable are referred to as formulas. This seems to be the case for every well-known identity I can think of, like the quadratic equation/formula. Can you think of any counterexamples?
The use of β=β for assignment in programming languages comes, not directly from mathematics, but indirectly from the use of mathematics in science and engineering. As an example, consider the formula for kinetic energy, commonly written
Why isn't it written 2K=mvΒ², which expresses the same mathematical equality in a smaller, simpler form? Or any of the other equivalent rearrangements? It's because formulas have a convention, where the LHS is a single term naming the value you want, and the RHS contains the terms for values you have. That is, a formula doesn't just state an equality, it states a method for calculating something. That usage predates programming, and was explicitly copied by early programming languages like For[mula]tran[slator] that were designed for scientific & engineering calculations.