>2+2=4>2x2=4is this coincidence or is there a deeper meaning to this?
>>16523683●●●●
>>16523683It's a consequence of both operators having two inputs, which is also the quantity for all inputs.
>>165236932/2 has two inputs and it's equal to 1
>>16523683>2^2 = 4>2^^2 = 4>... the ride never stops
[math]x + x = x \cdot x \\2x = x^2 \\x^2 - 2x = 0 \\x (x - 2) = 0[/math]Therefore the only solutions are [math]x = 0[/math] and [math]x = 2[/math].
>>16523832isn't it wild that only 0 and 2 are solutions? why do you think that is?
>>16523683>[math]\sqrt{3}[/math] x [math]\sqrt{3}[/math] x [math]\sqrt{3}[/math] = 5.1961524(...)>[math]\sqrt{3}[/math] + [math]\sqrt{3}[/math] + [math]\sqrt{3}[/math] = 5.1961524(...)Bros...
>>16523683No, its not a coincidence that two twos is the same thing as two twos, its the law of identity, I don't know how "deep" you believe that law of logic to be, but its one of (if not) the most fundamental rules of logic there is.
>>16523683>>16523865Same for 4 cubic roots of 4. Notice a pattern yet?
>>16523865this is nuts
>>16524295>>16523865>>16524311Yes the numbers for which "multiplying it X times is equal to adding it X times" are the (X-1)th roots of X and 2 is the only number where you get a (2-1)=1th root and therefore an integer. Except 1 because 1 times nothing = 1 plus nothing but Big Multiplication won't tell you that
>>16523683you're almost there...
[math]\forall n\in\mathbb{Z}^+, 2 \uparrow^{(n)}2 = 2+2[\math]
>>16524378[math]\forall n\in\mathbb{Z}^+, 2 \uparrow^{(n)}2 = 2+2[/math]
>>16523848Because x^2 - 2x is a parabola, and the two operations are equal only where the parabola intercepts the x-axis
>>16525112Wow, do you think we’ll ever understand what makes this happen?
>>16525157A. GodB. Systemic framework of logic, more fundamental even than God
>>16525194I don’t believe in ancient superstitions like “God” or “Logic”, tell me what the Modern explanation is!
>>16523790No shit retard, addition and multiplication are the same things, division isn't.
>>16523689fpbp/thread
that's actually insane
>>16523683It means square is optimal thing. Chew some squares yourself and you'll see.
You forgot exponentiation and tetration.The pattern is literally n/a,4,4,4,4,16 because fuck you.
>>16525272Because black science man has a calculator.There, nigger, happy? Or dost thou feel fine to say there exists no modern explanation?
>>16523683>piss comes out my dick>cum comes out my dickis this coincidence or is there a deeper meaning to this?
>>16525458I don't understand
2^4 = 4^2 = 16And that's the only non-trivial integer solution to the equation x^y = y^x.
>>16526208plot:https://www.wolframalpha.com/input?i=Plot%5Bx%5E%281%2Fx%29%2C%7Bx%2C0%2C10%7D%5DThe maximum is at x = e.
>>16525112interetsing
>>16526208why are there these random quirks to maths?
>>165236832 x N = N + N
>>16525272>I don’t believe in ancient superstitions like “Logic”the absolute state of /sci/.... is this a reflection of contemporary academia?
wait until you find out about 142857really i'm surprised there isn't at least one religious cult based around it
>>16523683Is this a science board still, or am I on the wrong board? Aren't we supposed to ask intelligent questions?
>>16529632why is this a dumb question? do you have an answer? because if you don't have an answer then it can't be an easy question
Satan's chosen jonspirators
>>16525194>God obeys traditional logicLol.. Lmao
>>16523683>2^4 = 4^2What the fuck?!
2 plus 2 is twenty two because when i write down the number two and then write down another two its the number 22 not four Your move
>>16530156it's less "off topic" than a "bump"the following reply settled everything>>16523832there was nothing left to write thereafterthe following reply is also "off topic">>16523865and no one complained about that
>>16523683https://youtu.be/2w6kHS_IRrE
>>165301564 ^ (4 + 4) = (4 * 4) ^ 4oh fuck
>>16530160there is some truth to this. 22 should mean 4 not 2x10+2
>>16530270oh fuck oh fuck oh shit OH SHI-
>>16529567Logic doesn’t follow DEI principles
>>165236833x3 = 3+3+32x3 = 2+2+22x2 = 2+2Multiplication is iterative addition.
>>16530270n ^ (n + n) = (n * n) ^ nOr:n^(2*n) = (n^2)^nWhich is a special case of:a^(b*c) = (a^b)^cAnymore seventh grade math?
>>16530869yeah, but 3x3=9 while 3+3=6same thing applies to 2x3=6 and 2+3=5
>>16530950That’s a good point!
>>16531051Thank you friend, my mom says I'm very smart
>>16531060My mom also says you’re very smart
>>16525112what app is this?
>>16531339desmos.com
>>16531343thanks king
>>16530871just because you proved it using math that doesn't make it less amazing. he wasn't claiming it was impossible to prove
>>16532563oh yes he was!
>>16532563more "amazing" examples, or instances, of seventh grade math:5^(3+3) = (5*5)^3 = 156252^(5+5+5) = (2*2*2)^5 = 327683^(5+5) = (3*3)^5 = 590494^(4+4+4+4) = (4*4*4*4)^4 = 42949672963^(2+2+2+2+2) = (3*3*3*3*3)^2 = 590492^(3+3+3+3+3) = (2*2*2*2*2)^3 = 327685^(2+2+2) = (5*5*5)^2 = 15625
>>16533892>4^(4+4+4+4) = (4*4*4*4)^4 = 4294967296this one is crazy
>>16533892Dude you can't just spill out the inner secrets of the universe like that.Like Ancients surely once said,"The Numbers. What do they mean?!"
>>16533893>>16534735enough of: a^(b*c) = (a^b)^ci hope this thread gets archived soon
>>16525157Please shut the hell up you dumb autistic fuck
>>16534789unlikely since you keep bumping it>>16534795have you taken your anger medications today or did you forget again?
>>16529608explain
>>16536240142857 is a cyclic numbertry multiplying it by 2, 3, 4, etcthen use a calculator to try 1/7, 2/7, 3/7 etcthen try 1/7, 1/(2*7), 1/(3*7), 1/(4*7) etc
>>16536247I don't have a calculator
>>16536253use your amazing human brain
>>16523683>is there a deeper meaning to this?Multiplication is just shorthand for addition.3 x 5 = 15 is shorthand for 3 + 3 + 3 + 3 + 3 = 15 so2 x 2 = 4 is shorthand for 2 + 2 = 4there is no deeper meaning
>>16536367>3 x 5 = 15>is shorthand for>3 + 3 + 3 + 3 + 3 = 15no, it's notit's shorthand for:5 + 5 + 5 = 15
>>16536391You say tuh·may·tow I say tuh·ma·tow, same thing tomato3 x 5 = 5 x 3 = 15
Aha, I've already got an answer for that!X+X=X*X 2X = X^2X=2X+X+X=X*X*X3X = X^3X=3^(1/2)Or the square root of 3.X+X+X+X=X*X*X*X4X = X^4X=4^(1/3)Or the cube root of 4.X+X+X+X+X=X*X*X*X*X5X = X^5X=5^(1/4)Seeing the pattern?N*X=X^NX=N^(1/(N-1))
>>165364003*5 = 5 + 5 + 55*3 = 3 + 3 + 3 + 3 + 3since 2*y = y + y for examplei didn't know, that Saturn has a hexagonal polar patch
>>16536472>i didn't know,>that Saturn has>a hexagonal polar patchHere is something else you do not know.MOST stars in the universe are red dwarfs.You can not see any red dwarfs with your eyes at night.NO red dwarf has 'died' of old age since the universe began.Basically if red dwarfs were humans they would all be pre-school toddlers.
>>16523683Both are equal to 2^2
>>16536500>Both are equal to 2^2Again exponentiation is just shorthand for multiple multiplication 10^5 = 10 x 10 x 10 x 10 x 10 = 100,000so 2^2 = 4is short hand for 2 x 2 = 4is short hand for 2 + 2 = 4there is no deeper meaning
>>16536524>so>2^2 = 4>is short hand for>2 x 2 = 4>is short hand for>2 + 2 = 4>there is no deeper meaningAha, but is there SUB-EXPONENTIATION?^ Powers* Multiplication + AdditionUpwards beyond exponents, there is tetration.3^3^3There should be something above tetration. What is below addition as a function?Can it really be turtles all the way down or is there only the wall of addition/subtraction?
>>16536622You are free to invent any new shorthand symbols if you want.
>>16536622+n and -n are inverses*n and /n are inverses^n and ^(1/n) are inversesand in calculus:I(_) and d(_) are inverses
>>165236832x2 means there are two 2's, i.e. 2+2. 2x2=2+2 by the definition of multiplication.No
>>16536367>>16536524>>16536731then what does 1.7x3.6 mean? you can't sum a number 3.6 times. this is what I mean when I say multiplication has a deeper meaning than that
>>165371421.7×3.6 = 3×3×17÷5÷5Thus division is also involved.I believe, that trigonometry is beneath, or behind, number theory.That trigonometry is the deeper, or underlying, thing.
>>16537142>then what does 1.7x3.6 mean?I do not get it? Is the decimal point bothering you?just move the decimal point over then restore it.1.7 x 10 = 17 3.6 x 10 = 36so our result will be 10 x 10 = 100 times bigger (move decimal 2 places to get correct answer)17 x 36 = 612612 / 100 = 6.12 (moved decimal 2 places to get correct answer)therefore1.7 x 3.6 = 6.12
>>165236830/0=0 (undefined)0+0=00-0=00x0=00^0=0 (undefined)1/1=11x1=11^1=12x2=42^2=42+2=43-3=03/3=0etc, every number from 3 and after only has two equal outputs from self-operations.Indeed 0, 1 and 2 aren't ordinary numbers and do demonstrate many unique properties.
>>16538016ok, so what's exπ?
>>16538032>3/3=0lmao this is the level of the science board
>>16536367>PicrelTrue future mathematician:Pi cant be expressed as a fraction but I can make it an infinite sum of fractions so haha nigga.[math]\pi=4(\sum^{\infty}_{n=0}(\frac{(-1)^n}{2n+1})[/math]
>>16538052>>3/3=0>lmao this is the level of the science boardYet, you will happily say that 0!=1 simply because it's convention. Not because it makes any logical sense. There's definitely a trend going on there that you dismissed away with one typo.>>16538032Here is an expansion of your list -0-0 =00+0 =00/0 =0 (undefined)0x0 =00^0 =0 (undefined), 1 often given as result0! =0 (undefined), 1 often given as result0root0 =0 (undefined), other results are given7 same answers1-1 =01+1 =21/1 =11x1 =11^1 =11! =11root1 =15 same answers2-2 =02+2 =42/2 =12x2 =42^2 =42! =22root2 =1.414.. etc3 same answers3-3 =03+3 =63/3 =13x3 =93^3 =273! =63root3 =1.442.. etc2 same answers4-4 =04+4 =84/4 =14x4 =164^4 =2564! =244root4 =1.414.. etc0 same answersSo yeah, self-operations with the same answers decrease as the size of the natural number increases from 0 to 3.From 4 and above no natural numbers display that property.
>>16538046Two irrational numbers multiplied by each other, the result is another irrational number... There is no simpler way to express the answer than 'exπ'You can get a rational number approximation as close add you would like, ~ 8.539What are you attempting to say or show?Is multiplication confusing to you?Are irrational numbers confusing to you????
>>16538643I'm saying multiplication is not addition chud, 2x2 doesn't mean 2+2 because otherwise exπ would be undefined
