>the explanation is trivial and is left as an exercise

>op is a faggot

>>8973075
Those are my favourite textbooks. They don't waste my time with trifles.

>tfw to stupid to find the trivial proof

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>>8973075 (OP)
>the explanation is trivial and is left as an exercise to the reader

TFW you find it in Hardcore Math books/papers such as
Algebraic Geometry or Shinichi Mochizuki's papers

By the way the pic is an excerpt from a Lecture Notes on Classical Algebraic Geometry by Stanford University
>https://web.stanford.edu/~tonyfeng/232a.pdf

Its written: "Proof. Left as an easy exericse."

And there is a typo, the professor spelled exercise wrong as "exericse".

>>8973434
top kek

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>>8973075
Definitions of Terms Commonly Used in Higher Math
>https://jcdverha.home.xs4all.nl/scijokes/1_7.html

Trivial = The student might be able to do it in 3 hours or so.
Simple = An "A" student can do it in a week or so.
Easy = This topic would make a good master's thesis.

It is obvious = Only to the Author of the textbook.
>or to PhD's who specialize in that field,
>or to instructors who have taught the course 100 times

The diligent student can show = It is an unsolved problem - probably harder than Fermat's Last Theorem.

>>8973075
>>8973454
>I'm too lazy to do shit and I only wanted to skim the book as if it was a novel

>>8973458

Proof: Check

Proof: Think

>>8973075
>From http://curiosamathematica.tumblr.com/post/122398968526/obvious

>An anecdotal story:

One day Shizuo Kakutani was teaching a class at Yale. He wrote down a lemma on the blackboard and announced that the proof was obvious. One student timidly raised his hand and said that it wasn’t obvious to him. Could Kakutani explain?

After several moments’ thought, Kakutani realized that he could not himself prove the lemma. He apologized, and said that he would report back at their next class meeting.

After class, Kakutani, went straight to his office. He labored for quite a time and found that he could not prove the pesky lemma. He skipped lunch and went to the library to track down the lemma. After much work, he finally found the original paper. The lemma was stated clearly and succinctly. For the proof, the author had written “Exercise for the reader”.

The author of this 1941 paper was Kakutani.

From Mathematical Apocrypha by Steven Krantz.

>>8973075
"Trivial" means that you'll get there if you just mindlessly follow the definitions.

>>8973434
This people really can't be bothered with brainlets.

>>8973126
Cuck.

>>8973502
>This people
checks out

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>>8973706
Brainlet.

>>8973434
yeah but those are actually really easy to prove.
and so what if a mathematician makes a spelling mistake? get fukt

>>8973730
I'm not the one who has to learn out of textbooks.

>>8973735
What do you learn "out of" then, brainlet?

>>8973743
I learn from the aether

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>>8973434
(i) no prime ideal contains the whole ring, every prime ideal contains the trivial ideal.
(ii) [math]\mathfrak{p} \in V(\bigcup_\alpha I_\alpha)\Leftrightarrow \bigcup_\alpha I_\alpha \subset \mathfrak{p} \Leftrightarrow \forall\alpha : I_\alpha\subset\mathfrak{p} \Leftrightarrow \forall\alpha : \mathfrak{p}\in V(I_\alpha) \Leftrightarrow \mathfrak{p} \in \bigcap_\alpha V(I_\alpha)[/math]
(iii) suppose [math]\mathfrak{p}\in V(I_1\cap I_2)[/math] and [math]\mathfrak{p}\not\in V(I_1)[/math]. If now [math]\mathfrak{p}\not\in V(I_2)[/math], then there are elements [math]a\in I_1, b\in I_2[/math] such that [math]a\not\in\mathfrak{p}\not\ni b[/math], but [math]ab\in I_1\cap I_2\subset\mathfrak{p}[/math], which is a contradiction, and so [math]V(I_1\cap I_2)\subset V(I_1)\cup V(I_2)[/math]. On the other hand, if [math]\mathfrak{p}\in V(I_1)\cup V(I_2)[/math], we may assume [math]\mathfrak{p}\in V(I_1)\subset V(I_1\cap I_2)[/math], and so [math]V(I_1)\cup V(I_2)\subset V(I_1\cap I_2)[/math].

The proof took about 10 minutes. You actually missed a typo. [math]\bigcup_\alpha I[/math] should be [math]\bigcup_\alpha I_\alpha[/math].

>>8973434
I hate algebra so fucking much

>>8974568
That's geometry.

>>8974470
high iq ubermensch

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>>8973473
This sounds like something from a /sci/ humor thread. I chuckled.

Take your pedophile cartoons back to >>>/a/

>>8974775
>algebraic geometry doesn't involve algebra
I hate you so fucking much