# 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 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. – Peter Woolfitt 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. – steven gregory 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. – Jyrki Lahtonen Sep 1 '15 at 18:19
• Editing and replacing with $2 \mapsto 6$ could be a solution. – Alex M. 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? – Joel Reyes Noche 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. – Jyrki Lahtonen Sep 23 '16 at 4:21
• @JyrkiLahtonen, okay, thanks. – Joel Reyes Noche Sep 23 '16 at 6:12

• 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?" – steven gregory Sep 1 '15 at 21:33
• @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. – steven gregory Oct 6 '15 at 1:32