# abuse of equal signs

I am referring to questions like THIS

Expressions like "3 = 6" are an abuse of notation and, as such, make doing mathematics correctly harder instead of easier.

Mathematics is peppered with mathematicians abusing notation, often justifying their actions by saying that "the context" should make what they mean clear. Usually it does. Puzzles like the one I referenced above abuse notation with no preamble.

I guess what I'm asking is, could I edit the question by appending a comment that the question might make more sense if, instead of

2 = 6
3 = 12
4 = 20

They thought of it as

2 becomes 6
3 becomes 12
4 becomes 20

or some such thing.

• Downvote, vote to close, flag as low quality, vote to delete, move on. That's not a mathematical question.
– Asaf Karagila Mod
Sep 1 '15 at 16:40
• Instead of "2 becomes 6" type statements, you could just turn it into a function: $f(2)=6$, $f(3)=12$, etc. Of course then the arbitrary nature becomes more obvious. Sep 1 '15 at 16:44
• @PeterWoolfitt Yes, but I was thinking of people who see that question and have only a vague idea of what a function is. They are capable of solving the puzzle, but now they have a distorted idea of what "=" means. Sep 1 '15 at 16:52
• Steven: You may find this thread in MathEducators.SE interesting. FWIW I just downvoted that question. Didn't like it at all. Sep 1 '15 at 18:19
• Editing and replacing with $2 \mapsto 6$ could be a solution. Sep 2 '15 at 12:24
• @JyrkiLahtonen, in your comment above, you say "I just downvoted that question. Didn't like it at all." Are you referring to the Mathematics Educators question that you linked to? Sep 23 '16 at 1:03
• @JoelReyesNoche: Sorry about using a pronoun hastily. This was a year ago, but I still remember clearly that I downvoted the question referred to in the above post. The post in MathEducators.SE OTOH - I have referred lecturer colleagues to it, and we discussed it during a coffee break. Sep 23 '16 at 4:21
• @JyrkiLahtonen, okay, thanks. Sep 23 '16 at 6:12

I think it is fine and useful to point out that the notation in the puzzle does not follow usual practice, and the equal-sign would better be a becomes or, say, an arrow.

This is a sufficiently basic thing that also for a user asking this question it is relevant information they likely can appreciate.

By contrast remarks like this being not a series (as mentioned in a comment) are in my opinion slightly besides the point.

The most natural way to leave such information is via a comment, but an edit seems alright too (especially if it is clear, as in this case, that the puzzle is not distorted by it).

• I think, even if they don't understand functions, that they interpret 2 = 6 as "you do something to 2 and you get 6". Then when they solve their first equation and they get x = 6. They interpret that as "you do something to x and you get 6". This is obviously very confusing. This is why, when they see $(x^2)^5$ they ask, "How do you solve this?" Sep 1 '15 at 21:33
• Yes, I agree, this is a problem. The MESE thread linked above discusses the issue in detail.
– quid Mod
Sep 1 '15 at 22:07
• I'm sorry to see the question closed as off topic. It's an honest question by someone trying to understand maths. There is a decent answer there which encourages the asker in their approach. And, yes, an explanation about notation would be appropriate. Sep 19 '15 at 17:32
• @AdamHrankowski I have taught and tutored a lot of mathematics over the years. It took me a while, but it finally occurred to me that my students did not really understand what "$=$" meant. I see these problems and it offends my mathematical sensibilities like a fingernail across a blackboard. Oct 6 '15 at 1:32