/sci/ - Science & Math

[Anonymous No.8973075]

>the explanation is trivial and is left as an exercise to the reader

[Anonymous No.8973077]

>op is a faggot

[Anonymous No.8973126]

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

[Anonymous No.8973403]

>tfw to stupid to find the trivial proof

[. No.8973433]

>>8973075
>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

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

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

[. No.8973434]

>>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".

[Anonymous No.8973445]

>>8973434
top kek

[. No.8973454]

>>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.

[Anonymous No.8973456]

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

[Anonymous No.8973458]

[. No.8973467]

>>8973458

Proof: Check

Proof: Think

[. No.8973470]

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

One day Professor 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.

[. No.8973473]

>>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.

[Anonymous No.8973500]

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

[Anonymous No.8973502]

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

[Anonymous No.8973706]

>>8973126
Cuck.

[Anonymous No.8973707]

>>8973502
>This people
checks out

[Anonymous No.8973730]

>>8973706
Brainlet.

[Anonymous No.8973734]

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

[Anonymous No.8973735]

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

[Anonymous No.8973743]

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

[Anonymous No.8973751]

>>8973743
I learn from the aether

[Anonymous No.8974470]

>>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].

[Anonymous No.8974568]

>>8973434
I hate algebra so fucking much

[Anonymous No.8974775]

>>8974568
That's geometry.

[Anonymous No.8976346]

>>8974470
high iq ubermensch

[Anonymous No.8976435]

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

[Anonymous No.8976509]

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

[Anonymous No.8978423]

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