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How to read math. You’d be surprised how far this will get you.
[Isn’t the last one “for all integers a and b there exists a unique positive integer k such that …..”? I think maybe you meant to not have the superscript +?]
I think there was supposed to be a plus, and that it was supposed to have your correction. In any case, it is false: there is no gcd(0, 0). Other than that edge case, though, all GCDs are positive.
Similarly, the subset sign used in saying the reals are a subset of the reals usually means “proper subset”, which is a non-equal subset; this is clearly false. The one used in the glossary part means any subset and would have worked. Think of the difference between the less-than sign (<) and the less-than-or-equal-to sign (≤): the bar means the same thing in both cases.
EDIT TO ADD: Still very good and gets the main points across nicely.
EDIT: Tumblr ate some of my post and formatting because I didn’t realize I was in the HTML editor mode. I fixed them.
daniel-r-h has some good points.
- The first statement is not a true statement (which is my bad). However, it is almost translated correctly (I believe). As transgeometer points out, there’s something going on with the superscript and the positivity of k. I intended the superscript because the gcd should be positive, but failed to translate it properly and say a “unique positive integer k.”
- The second point about the subsets is also technically correct, but… the translation is still correct in a way too. Notice how the glossary symbol for “subset of” has a line under where as the example does not. Some mathematicians interpret there being no line under the symbol as meaning the set has to be a proper subset, meaning the subset cannot be the entire set. However, there are many mathematicians that use both symbols interchangeably. When they want to indicate that they are looking at proper subsets, they use another symbol which has a line with a slash through it. I think it’s important to be told this because until someone does, you can ask the kind of questions that daniel-r-h did about proper and not proper subsets, when the writer is just using their preference of subset symbol. I’ll admit it was a mistake when I typed it up though (\subset and \subsetneq)
Thank you for pointing out these mistakes though! You’re better mathematicians than me
so che, dopo anni di tumblr, la cosa non dovrebbe stupirmi, ma il gatto salta sull’acqua.
"Il basilisco piumato (Basiliscus plumifrons Cope, 1876) è un rettile dell’ordine degli Squamati (sottordine Lacertilia, infraordine Iguania) diffuso in Centro America.Viene soprannominata "lucertola di Gesù Cristo" per la particolare abilità di camminare sull’acqua, grazie alla particolare conformazione delle quattro zampe che riescono a trattenere delle piccole bolle d’aria sotto il palmo."
"LUCERTOLA DI GESU’ CRISTO" che fra l’altro è una cosa che dico spesso durante la giornata.
"Man Size" - One Gallon
DOMESTICATED TIGER DOMESTICATED TIGER.
Lijiang Xu House Li Xiaodong Atelier