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Simplify (sh.itjust.works)
submitted 1 month ago by sjmarf@sh.itjust.works to c/mathmemes
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[-] greybeard@lemmy.one 173 points 1 month ago

For those of you who were confused even after reading the comments: (a)(b) basically means a*b. My mind just didn't connect that to the fact that (x-x)=0. in the (a-x)(b-x) stuff is also (x-x) which = 0, and anything * 0 = 0, so no matter the value of literally everything else in the equation, it all equals out to 0 because every single () will get multiplied by (x-x), which is 0. There, hopefully that will clear it up for anyone remaining lost. And like all good jokes, they are always best when you have to explain them.

[-] MonkderVierte@lemmy.ml 10 points 1 month ago

(a)(b) basically means a*b

Ok, wtf. Why write it like this then?

[-] superkret@feddit.org 28 points 1 month ago

To make sure what's inside the brackets is resolved internally before they're multiplied with each other.

 (a)  (b)   =   a * b  
(a+1)(b+1) =/= a+1*b+1
[-] brbposting@sh.itjust.works 2 points 1 month ago* (last edited 1 month ago)

TIL this notation makes it math the text up

(a)  (b)   =   a * b  
    (a+1)(b+1) =/= a+1*b+1

Edit: hmm, already shows in a code block so adding backticks didn’t do anything

[-] greybeard@lemmy.one 7 points 1 month ago* (last edited 1 month ago)

To expand on what superkret said, in math there is the concept of "order of operations". That is to say, every function in math (add, multiply, divide) has to be done in a specific order. Since multiplication comes before addition and subtraction, if you have a formula like a-x*b-x, you will do x*b first, then a minus the result of x*b, which would give a very different result than if you did a-x and multiplied that by b-x. This is where the parenthesis come in. You are basically saying, resolve every section in parenthesis first using the proper order, then resolve the rest.

My original example (a)(b) was over simplified, because there is no conflict there. You can also do things like (a*x)-(b*x). If there is no operator though, it is assumed multiplication, and I'm unsure why that is.

[-] starman2112@sh.itjust.works 4 points 1 month ago* (last edited 1 month ago)

Putting multiple asterisks in a comment makes it look italicized, at least on some Lemmy clients. If you want to have asterisks with *unitalicized* text, you gotta put a \ behind the * to negate the change

[-] greybeard@lemmy.one 3 points 1 month ago

Oops, I should have previewed it, thanks for pointing it out.

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[-] Jyek@sh.itjust.works 3 points 1 month ago

Because you wrote a lot less when writing it this way. Groups of terms beside each other are multiplying each other and you have to solve what's inside of those groups before multiplying them together.

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[-] Saganaki@lemmy.one 88 points 1 month ago

For those that struggled like me…

Going from a-z, write out the last three multiplicands.

[-] dditty@lemm.ee 54 points 1 month ago
[-] sem 2 points 3 weeks ago

For those of you who still struggled like me, a multiplicand in this case refers to one of the (n-x) terms.

[-] SmartmanApps@programming.dev 3 points 3 weeks ago

a multiplicand in this case refers to one of the (n-x) terms

Well, that's what was apparently meant, but in fact the correct terminology here is factors. There's only multiplicands (and multipliers) with an explicit multiplication sign. axb - multiplicand a and multiplier b, ab - Term with factors a and b, and a is the coefficient of this Term.

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[-] the_tab_key@lemmy.world 53 points 1 month ago

Even if the x-x term didn't exist, the equation is already simplified (fully factored) so there is nothing to do anyway.

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[-] LostXOR@fedia.io 47 points 1 month ago

Fun fact, omitting the (x-x) zero term and expanding the entire polynomial, you'd get something with 2^25 = 33,554,432 terms. May be slightly excessive!

Couldn't you combine a lot of like terms as you went along, though? A polynomial of the order x^26^ would only have 27 terms.

[-] LostXOR@fedia.io 2 points 1 month ago

No, because each coefficient is its own variable; they're not constants.

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[-] SmartmanApps@programming.dev 2 points 3 weeks ago

33,554,432 terms

Actually it would be that many factors. The whole thing is a single Term.

[-] disguy_ovahea@lemmy.world 41 points 1 month ago

This was impossible to answer prior to 3 BC.

[-] anzo@programming.dev 16 points 1 month ago

Unless you were Mayan. They had a concept of zero, or so I heard. But they lacked the letters, a-z and the parentheses :p

[-] magic_lobster_party@fedia.io 36 points 1 month ago

0 wasn’t invented yet.

Mesopotamians invented it because year 0 was approaching, so there was a dire need to represent such number.

[-] scapegarced@sopuli.xyz 2 points 1 month ago

TIL they had ghost concerts back then

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[-] disguy_ovahea@lemmy.world 6 points 1 month ago

That’s when the number 0 was introduced in India.

Ah, I forgot zero was so recent.

[-] atro_city@fedia.io 14 points 1 month ago
[-] magic_lobster_party@fedia.io 64 points 1 month ago

0

There’s an (x - x) in there

[-] copd@lemmy.world 13 points 1 month ago* (last edited 1 month ago)

Technically there is a (x - 𝑥) in there. U+1D465 != x so this post is a little meh

[-] MBM@lemmings.world 11 points 1 month ago

Mathematicians do weird stuff to get more letters, but I've never seen anyone use x and 𝑥 for different things

I've never seen anyone use x and 𝑥 for different things

Yeah, me neither. I have had situations where I needed to distinguish between u, v, nu, and upsilon though. I had to be very careful with my handwriting that day...

[-] joshthewaster@lemmy.world 4 points 1 month ago

They also wouldn't want to be ambiguous. If I was trying to write this problem the a, b, c... would get replaced by something like a_1, a_2,..., a_26 to be clearer. This problem works as a fun gotcha but isn't something that would come up in the real world.

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[-] shasta@lemm.ee 2 points 1 month ago

Assuming both x represent the same number. There's no reason to assume the ellipses should include x-x. Why would alphabetic order be involved at all?

[-] pyre@lemmy.world 7 points 1 month ago

have you never taken math? I'm seriously asking because you're incredibly wrong in both statements.

[-] cypherpunks@lemmy.ml 5 points 1 month ago

Why would alphabetic order be involved at all?

Because the ... notation effectively means: fill in the blanks. See https://en.wikipedia.org/wiki/Ellipsis#In_mathematical_notation (or https://en.wikipedia.org/wiki/Iterated_binary_operation if you want more...)

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[-] sag@lemm.ee 5 points 1 month ago
[-] MyTurtleSwimsUpsideDown@fedia.io 2 points 1 month ago

Now I want pie.

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this post was submitted on 23 Nov 2024
331 points (100.0% liked)

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