[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 527 KB, 1280x800, 001.jpg [View same] [iqdb] [saucenao] [google]
5316265 No.5316265 [Reply] [Original]

> multiplication is just repeated addition
true or false

>> No.5316288

true

>> No.5316286
File: 3 KB, 159x62, 1336792090827.jpg [View same] [iqdb] [saucenao] [google]
5316286

Going with true.

Monitoring this thread.

>> No.5316295

>Subtraction is just adding negative numbers

>Division is just the opposite of multiplication

So you can only add numbers?

>> No.5316297

true on the naturals
false on the reals

>> No.5316311

>>5316297
/thread

>> No.5316316

>>5316297
> implying the reals exist

>> No.5316318

Ring, Ring! Abstract Algebra here.

>> No.5316344

>>5316316
>implying numbers exist

>> No.5316362

>>5316344
>implying existence exists

>> No.5316369

>>5316316
>>5316344
>>5316362

I fucking love you guys

>> No.5316379

>>5316362
Ring! Ring! Ayn Rang here. Rand. Ayn Rand here.

>> No.5316381

>>5316362
>implying implying exists

>> No.5316384 [DELETED] 

>>5316369
>>>/b/
>>>/reddit/

>> No.5316390

>>5316265
False.

/thread

>> No.5316395
File: 142 KB, 949x768, 1249547860901.jpg [View same] [iqdb] [saucenao] [google]
5316395

>>5316265
Exponents are just repeated multiplication

Nested loops, nested loops everywhere!

>> No.5316400
File: 6 KB, 200x291, 1344281539645.jpg [View same] [iqdb] [saucenao] [google]
5316400

>>5316316
>implying your brain is manifested out of the imaginary

>> No.5316404

>>5316265
False. Over the natural numbers this is true, as >>5316297 stated, but over a general ring (or even a group) multiplication is a completely different operation. In fact, we often just denote the two operations as addition and subtraction because it's easy and to emphasize that we're dealing with two different binary operators.
Many times the "multiplication" in a group can actually be composition, as with functions.

>> No.5316414

>>5316395
Exponents ARE repeated multiplication. That's their definition.

>> No.5316417 [DELETED] 

>>5316297
I was making a similar argument to the one OP is posting in a different thread. Somebody responded similarly to your post (maybe it was you) saying basically it's true for natural numbers but doesn't really have any relation to what it means to raise something to the power of e, or pi, etc. Yet intuitively I still think that of course raising <span class="math">2^{e}
will be more than 4 but less than 8...

Anyway I'm not trying to be difficult or contrary...would you mind explaining at what level of math or in what courses one might get an intuition for what it 'means' to perform these operations on the reals?[/spoiler]

>> No.5316424

>>5316414
Not quite, exponentiation is defined differently for negative and positive numbers

>> No.5316426

You forgot about addition being iterative counting

>> No.5316428

>>5316297
woops i just typed out a reply but deleted it cause i think i fucked up the latex tags...

short version:
at what level math/what kind of course would i learn what it 'means' to perform these operations on the reals. two to the power e is more than 4 but less than 8, but really hwat's going on?

>> No.5316430

i * i

How do I add i to itself i times?

>> No.5316431

>>5316414
How do you multiply something with itself negative one times?

http://www.maa.org/devlin/devlin_01_11.html
This may be of interest to this thread.

>> No.5316434
File: 77 KB, 333x333, 1348178992197.jpg [View same] [iqdb] [saucenao] [google]
5316434

>>5316426
How come we can iterate a function?

>> No.5316437

>>5316414
No, it isn't.

e^(pi * i)

>> No.5316444

>>5316434
Memory?

>> No.5316446

>>5316424
But negative exponents are simply multiplication by the inverse

>> No.5316448

>>5316437
<span class="math">e^{i*\pi}=3[/spoiler]

>> No.5316463

>>5316448
You what now

>> No.5316466

>>5316437
> implying that isn't defined by an infinite series = ADDITION
you just told yourself exponentially

>> No.5316468

>>5316463
First time I saw Euler's glorious and beautiful identity was hard for me to handle too. Just stare it for a while and maybe the beauty will slowly dawn on you.

Tomorrow I am going to a tattoo parlor to get these beautiful expression tattooed upon my taint.

>> No.5316483

>>5316466
Using the rules that a) exponentiation is repeated multiplication and b) that multiplication is repeated addition, can you prove that?

(That is, can you show that e^i*x has the Taylor series it does using the above rules?)

>> No.5316493

>>5316468
except e^(i*pi) = -1

you fucking mongrel.

>> No.5316497

>>5316483
just define it as the taylor series, that is arbitrary

>> No.5316505

>>5316431
actual /thread

>> No.5316516

>>5316434
You need zero, the successor function, and a recursion function.

>> No.5316535

>>5316483
I guess that depends on whether you think something like Peano arithmetic is a sufficient basis for doing mathematics. What do you think?

>> No.5316542

>>5316493
i think it makes people so angry because it simultaneously misquotes euler's identity while also creating a 'pi is exactly 3' association

>> No.5316556

>>5316318
A bit late, but I see what you did there and it is glorious.

>> No.5316572

>>5316448
What.

Exactly 3?

What. That's impossible.

...HOW

WHY

>> No.5316575

>>5316505
> multiplication by negative one
> /thread
choose 1. Define the integers as pairs of naturals, guess what, integer multiplication is just addition and multiplication on pairs of naturals which is... drumroll... wait for it... waaaait for it...

>> No.5316605

>>5316572
>e^(2pi*i) = 1
>2pi*i = log 1 = 0
>either 2, pi, or i = 0

>> No.5316695
File: 237 KB, 467x329, amazingatheist.png [View same] [iqdb] [saucenao] [google]
5316695

>>5316605

>> No.5316765

false
>multiplying two decimals cannot be added

>> No.5316768

>>5316765
you'd be surprised

>> No.5316815

>>5316605
>not using the complex logarithm
absolutely disgusting.

>> No.5317732

>>5316815
> the complex logarithm
> of 1
math fan detected

>> No.5317738

Multiplication is linear interpolation of repeated addition.

>> No.5317751

>>5317738
Awesomely true!

>> No.5317805

The product of groups certainly is not the repeated sum.

>> No.5317812

It's funny how when people talk about division by zero, and I bring up wheels and projective lines, everyone is like "b-but that's not wh-what we mean by d-division" and yet when someone says multiplication is repeated addition, which it plainly is and always has been as anyone can see from the definition for naturals, suddenly all the alternate definitions are the norm.