You Don't Say?

Sometimes there are many ideas in math that make you go

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This note is going to be all about the most obvious facts about math. Post the ones that you think are extremely obvious and vote up your favorites.

I am adding a few to get things moving.

Have fun and be totally obvious!

For those of you who want a link to the image - https://i.imgur.com/Fvnb0Xl.png.

#Math #JustForFun #Memes #Theory

Easy Math Editor

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Comments

Jordan Curve Theorem

Every closed non-self intersecting continuous loop on the plane divides it into an interior and exterior region, i.e. inside and outside the loop. Proofs of it are some of the longest, most difficult ones in mathematics, usually involving algebraic topology.

Axiom of Choice

Given any number of non-empty sets, it's possible to pick exactly one member from each of those sets, which makes for a new non-empty set. That is, given a lot of boxes, all of them with things in it, I can get another box, and pick one item from all the other boxes and put them into this box. No proof exists for this one, so it has to be made into an axiom.

Michael Mendrin - 7 years ago

I wish I could upvote you again and again! This is gold!

Mursalin Habib - 7 years ago

$\displaystyle 0\times \pi\times \tau\times \phi\times e = 0$

$\displaystyle\text{MIND = BLOWN}$

Anish Puthuraya - 7 years ago

The Pigeonhole Principle

If you have things stuffed in containers and if there are more things than containers, then at least one container has more than one thing in it.

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Mursalin Habib - 7 years ago

PHP wins in my opinion :D

Eddie The Head - 7 years ago

agreed

Yan Yau Cheng - 7 years ago

@Yan Yau Cheng – agreed

Cody Johnson - 7 years ago

Reflexive property of equality

$a=a$

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Mursalin Habib - 7 years ago

The obvious one is

$1 + 1 = 2.$

ON page 357 of Principia Mathematica, they finally conclude

From this proposition it will follow, when arithmetical addition has been defined, that $1+1=2$ .

Calvin Lin Staff - 7 years ago

And then came along Kurt Godel.

Michael Mendrin - 7 years ago

$\displaystyle 1+1 = 2$

Anish Puthuraya - 7 years ago

haha! this is what even i thought immediately after reading this post.. :P :P

Pradeep Ch - 7 years ago

Lol, same here!

Robert Fritz - 7 years ago

Intermediate Value Theorem

If a continuous function $f$ with an interval $[a, b]$ as its domain takes values $f(a)$ and $f(b)$ at each end of the interval, then it also takes any value between $f(a)$ and $f(b)$ at some point within the interval.

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Mursalin Habib - 7 years ago

Well, you often get to experience your teacher being Captain Obvious in your school. :P Here's something my "maths" teacher wrote on the blackboard while "teaching" us quadratics:

'If the product of two numbers is zero, one of them must be zero.'

And I was like: you don't say?

What's strange is that we always have to write this exact same line (its Bengali translation) whenever we're solving a quadratic otherwise we get a zero out of five, apparently because guys who think this is too obvious don't have any understanding of maths and just memorize stuff.

Oh, and here's another one. I found this in my eleventh grade "maths" textbook.

Law of trichotomy: Given any two real numbers $a,b,$ either $a>b$ or $a=b$ or $b>a.$

If you're thinking this isn't something important, well... I found out that there was an exercise at the end of the textbook which asked to state the law of trichotomy using examples. In fact that question appeared more than once in the eleventh grade final "maths" examination before.

Sreejato Bhattacharya - 7 years ago

সমাধান কর

$x^2-5x+6=0$

$\Rightarrow (x-2)(x-3)=0$

দুটি সংখ্যার গুণফল শূন্য হলে এদের মধ্যে কমপক্ষে একটির মান শূন্য হবে।

অর্থাৎ,

হয়, $x-2=0$ অথবা, $x-3=0$ .

সুতরাং, $x=2$ অথবা $x=3$ .

নির্ণেয় সমাধান $x=2, 3$ .

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Mursalin Habib - 7 years ago

"তোমার স্টেপ জাম্প হয়েছে। $x^2 - 5x + 6 = 0 \implies x^2 - 2x - 3x + 6 = 0 \\ \implies x( x-2) - 3 (x-2) = 0 \implies (x-2)(x-3)=0$ এই স্টেপটা না দেখালে নম্বর কাটা যাবে। " -- my maths teacher

I don't want to live on this planet anymore

Sreejato Bhattacharya - 7 years ago

@Sreejato Bhattacharya – এই জাম্পটা করলে ছোট ক্লাসে নাম্বার কাটা যেত। এখন আর কিছু বলে না। কারণ এই জিনিস তো আর সরাসরি পরীক্ষায় আসে না।

Mursalin Habib - 7 years ago

@Mursalin Habib – Amar maths teacher sasti dito erokom step jump korle.....bolto erokom korle madhyamik porikkhai number kata jabe....,

Eddie The Head - 7 years ago

@Eddie The Head – সব স্কুলের maths teacher গুলো অরকমই হয়। আমি RMO পেয়েছি শুনে আমার teacher বলল ওই problem গুলো নাকি S.N Deyর বইটাতে extensively cover করা আছে। -__-

Sreejato Bhattacharya - 7 years ago

@Sreejato Bhattacharya – S.N.Dey te RMO r onko? Eta boddo barabari hoye gelo.....ami paper dekhechi but S.N.Dey boddo pati boi......

Eddie The Head - 7 years ago

@Eddie The Head – jani. kintu school-er teacher guloo toh orokom. sarakkhon schooler vaater onkogulo koriye matha kharap kore chare. RMOr paper-er second questionta dekhe bole ota S.N Dey-r boi te ache, baki questiongulo ar dekheini. tokhoni bollo oi sob onko naki S.N Dey-te extensively cover kora ache, madhyamik-er age kore kono labh nei. -__-

Sreejato Bhattacharya - 7 years ago

@Sreejato Bhattacharya – Amio onek loceder lecture sunechi je "madhyamik er age kore labh nei blah blah".amar obhigota bole osob lokeder kothai ekdom kan dite nei.....age t heke kora thakle onek subidha hoi

Eddie The Head - 7 years ago

@Eddie The Head – se ekhaneo sobkota maal orokomi. INMOr age madhyamik madhyamik kore keu asol onko kortei dilo na.

Sreejato Bhattacharya - 7 years ago

@Sreejato Bhattacharya – Hahahhaha.....

Eddie The Head - 7 years ago

@Eddie The Head – (sorry, rag-er jore mukher bhasa saamlate parlam na.)

Sreejato Bhattacharya - 7 years ago

@Mursalin Habib – ক্লাস ১০-এ প্রচণ্ড ভুগতে হয়েছে এই ন্যাকামির পাল্লায় পরে। একটা পাতি quadratic solve করার জন্য আধ পাতা ভাটাতে হত। ১১-এ আর quadratic solve করতে দেয় না, কিন্তু তাও দেখছি অঙ্কের থেকে ন্যাকামো বেশী।

Sreejato Bhattacharya - 7 years ago

Amio bangali tai tomar betha bujhte perechhi

Rayeed Amir - 7 years ago

For anyone else is wondering what @Sreejato Bhattacharya , @Eddie The Head , and I are talking about, here is a short summary:

Depressing stuff, more depressing stuff, suicidal thoughts and finally more depressing stuff.

Mursalin Habib - 7 years ago

Haha. In a similar vein, when they teach induction in school, they are very pedantic about how the format of the proof should be written up, ranging from "state the proposition, prove the base case, prove the induction step, state the conclusion".

Calvin Lin Staff - 7 years ago

Yes indeed, that's very annoying. Also, whenever we're given to differentiate something, say $f(x) = x^2 + x + 1$ at $x=3,$ here's what we have to write (translated into English):

$\begin{array}{lll} f'(x) & = \dfrac{d}{dx} (x^2 + x + 1) & \quad \text{substituting } f(x) \\ & = \dfrac{d}{dx} x^2 + \dfrac{d}{dx} x + \dfrac{d}{dx} 1 & \quad \text{(the derivative of the sum of two functions is equal to the sum of the derivative of those functions)} \\ & = 2 \cdot x^{2-1} + 1 \cdot x^{1-1} + 0 & \quad (\dfrac{d}{dx} x^n = n x^{n-1} + \text{ and the derivative of the constant function is zero)} \\ & = 2x + 1 & \quad \text{(simplifying)} \\ f'(3) & = 2 \cdot 3 + 1 & \quad \text{(plugging } x=3 \text{)} \\ & = 7 \quad & \text{evaluating} \end{array}$

If we miss any of these "explanations", we lose marks. In general, the school curriculum is obsessed with jargon and nomenclature instead of mathematics itself.

Sreejato Bhattacharya - 7 years ago

@Sreejato Bhattacharya – This is so very true and proves that CBSE sucks! I once lost marks for not writing that I had simplifed an expression by multiplying both sides by the same number -_-

Krishna Ar - 6 years, 12 months ago

@Krishna Ar – @Krishna Ar D'you remember the ultra-sucking method they taught to prove that the sum of all the interior angles of a triangle is 180 degrees! And you'd lose half the marks if you don't mention that "since EF is a line parallel to the base BC of the triangle, and Ab is a transversal cutting the two parallel lines, the interior opposite angles DAB and ABE will be equal."

Satvik Golechha - 6 years, 12 months ago

@Satvik Golechha – And if this much torture wasn't enough, there are IIT coaching institutions to go to.

Sreejato Bhattacharya - 6 years, 12 months ago

@Satvik Golechha – Yup,correct!

Krishna Ar - 6 years, 12 months ago

@Krishna Ar – Not only CBSE. I study in WBBSE (West Bengal state board). I often got scolded while solving a linear equation in eighth grade for not writing "transposing" when adding both sides by a certain quantity, so I know that feel.

Sreejato Bhattacharya - 6 years, 12 months ago

@Sreejato Bhattacharya – Truly. But nothing can beat the suckiness of CBSE. The way they literally do nothing in 9 and 10 and stuff the heck out of the child in 11 and 12 is unpardonable.

Krishna Ar - 6 years, 12 months ago

@Sreejato Bhattacharya – I think you're exaggerating a little bit now.

Simplifying? Evaluating? Seroiusly?

Mursalin Habib - 7 years ago

@Mursalin Habib – Yes, seriously! (মান বসিয়ে পাই... না লিখলে ১ নম্বর কাটা )

Sreejato Bhattacharya - 7 years ago

@Sreejato Bhattacharya – আমি মান বসিয়ে পাই -এর কথা বলিনি [ওটা আমাদেরও লিখতে হত]। আমি বলেছি "সরলীকরণ করে", "মান নির্ণয় করে" এগুলোর কথা।

Mursalin Habib - 7 years ago

@Mursalin Habib – আমাদের-ও প্রত্যেক স্টেপএর পাশে "মান বসিয়ে পাই লিখতে" হয়। ওই "মান বসিয়ে পাই"-টাকেই ট্রান্সলেট করতে গিয়ে evaluating আর simplifying হয়ে গেছে, আর কোনো ভাল ইংরেজি শব্দ মাথায় এলো না। :P

Sreejato Bhattacharya - 7 years ago

There cannot exist an infinitely decreasing sequence of positive integers......

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Eddie The Head - 7 years ago

Prove it!

A Former Brilliant Member - 6 years, 12 months ago

Commutative Property of Addition :

If $a,b$ be two numbers, then $a+b=b+a$ .

Prasun Biswas - 7 years ago

In $2\text{-dimensional}$ space, given a line and a point not on the line, there is exactly one line passing through that point that is parallel to the given line.

I like this fact because it is so simple and yet the source of so much controversy. See here

Trevor B. - 7 years ago

If $a = b$ and $b = c$ , then $a = c$

Shabarish Ch - 7 years ago

Given any two numbers $a,b$ , either $a<b$ or $b\leq a$

Nanayaranaraknas Vahdam - 7 years ago

All positive odd integers can be expressed as the sum of two non-negative, consecutive integers that are less than or equal to it.

Finn Hulse - 7 years ago

What about $1$ ?

Jubayer Nirjhor - 7 years ago

What Finn was trying to say was this:

$2k+1=k+(k+1)$

But he didn't state properly.

Mursalin Habib - 7 years ago

@Mursalin Habib – Yes. What he missed is $2k+1 > k+1$ only when $k>0$ . He didn't deal with the $k=0$ case properly.

Jubayer Nirjhor - 7 years ago

@Mursalin Habib – Yeah but I said "non-negative".

Finn Hulse - 7 years ago

@Finn Hulse – I see that you have edited your comment. Initially it said that an odd positive integer can be expressed as the sum of two smaller non-negative consecutive integers, which isn't true for $1$ .

Mursalin Habib - 7 years ago

@Mursalin Habib – Yeah that's what I did.

Finn Hulse - 7 years ago

If $a=b$ , then for any function $f$ , we have that $f(a)=f(b).$ This same property is the one that we exploit when solving equations. (like when we add the same thing to both sides, if we multiply by the same number...)

حكيم الفيلسوف الضائع - 6 years, 12 months ago

Given any two real numbers $a,b$ , there exists a real number $n$ such that $a=b+n$