/sci/ - Science & Math

[Anonymous No.7259516]

why is 1/1 =1 and not 0? why is 1/0 not equal to 1?

inb4 ur a retard OP

[Anonymous No.7259520]

>>7259516
1/ 0 = 1, we should be able to multiply both sides by 0 and get an equally true statement, but instead we get 1 =0. So that's not true,

1/1 = 1 because 1 is the multiplicative identity- multiplying anything by 1 returns that anything. since x * 1 = x, divide both sides by x to get 1/ 1 = 1.

[Anonymous No.7259522]

>>7259516
think of division as producing a ratio between the numerator and denominator. n/n = 1, because the numerator and denominator are equal.

Division by zero is undefined.

[Anonymous No.7259526]

>>7259516
Pretty much anything divided by itself is one. This is because of what division actually is.

Division means to take a number and divide it into a certain number of portions, and the answer is the quantity any of those particular post-division portions would have.

So, let's say you have 30 items. And you divide it by 3. You would then have 3 lots of 10 items each. Hence, 30 / 3 = 10.

Now, let's look at 1. You divide it into 1 lot. Which means it stays as 1. Thus, 1 / 1 = 1.

Now, division by 0. The whole principle of division is based on the idea of dividing things into lots, then identifying the quantity in each lot as your answer. If you're dividing something into zero lots, then there are no lots, there are no quantities. It's not a matter of any of the lots having 1 in them, or having nothing in them. It's a matter of the lots just not existing. Hence, why the answer of anything divided by 0 is "undefined."

[Anonymous No.7259527]

>>7259516
if you share one apple between 2 persons, each gets 0.5 apple. if you share one apple between 1 person, each gets 1 apple. share one apple between 0 persons, and SYNTAX ERROR

[Anonymous No.7259532]

>>7259527
> share one apple between 0 persons
wouldnt there still be one apple?

>>7259520
1/0 =1 multiply by both sides makes sense, thanks

[Anonymous No.7259535]

>>7259526
>If you're dividing something into zero lots, then there are no lots, there are no quantities.
then why isnt 1/0 =0

[Anonymous No.7259546]

>>7259535
You have something, and you want to divide it such that you have 0 parts. It is not possible.

[Anonymous No.7259547]

>>7259535
>>7259532
But the apple hasn't been divided. You need to count the quantities post-division. If no division can occur, no counting can occur. If no counting can occur, then the answer is just, "undefined."

[Anonymous No.7259559]

>>7259516
1/1 means: divide one apple into one part, which gives you the same whole apple.

1/0 means: divide one apple into zero parts, which leaves you with zero.

[Anonymous No.7259572]

>>7259516
As much as it is meme math, Vihart did a pretty good video on the conceptual understanding of arithmetic and algebra

[Anonymous No.7259575]

>>7259559
>1/0 means: divide one apple into zero parts, which leaves you with zero.
While it is undefined, you'll find that dividing by numbers exceedingly close to 0 will yield infinity. This would suggest that anything divided by zero is infinity.

>inb4 infinity isn't an actual number

[Anonymous No.7259577]

>>7259516
By the definition of division, "x/y = z" means that z is the unique number such that x = yz. So, "1/1 = z" means z is the unique number such that 1 = 1z, so z = 1. Likewise, "1/0 = z" means z is the unique number such that 1 = 0z, but 0z = 0 for any number z, so there's no such number — the expression "1/0" doesn't refer to any number.

[Anonymous No.7259588]

>>7259577
Yes, but this definition is based on convenience. We use it because it doesn't break anything.

[Anonymous No.7259596]

>>7259588
We use it because it's consistent and useful.
It's the abstract definition of a field.

There are other structures that allow 1/0, a field isn't one of them.

[Anonymous No.7259649]

>>7259526
This is a fair enough answer, but one of the biggest things we did in the 20th century was to abstract the concept of arithmetic.
Formally speaking, division by zero is undefined because we're actually multiplying by zero-inverse. Call it <span class="math">0^{-1}[/spoiler].

Suppose such a number existed. By definition, we know that <span class="math">0\cdot 0^{-1}=1[/spoiler]. But this violates another of our assumptions that <span class="math">\forall x \in \mathbb{R}, x\cdot 0 = 0[/spoiler].
In other words: it'd be impossible to define an Abelian ring if we allowed a <span class="math">0^{-1}[/spoiler]. And since we get a lot of nice properties by making <span class="math">\mathbb{R}[/spoiler] into an Abelian ring, we are forced to say that <span class="math">0^{-1}[/spoiler] does not exist.

[Anonymous No.7259662]

>>7259649

But anon, 0-1 is -1. Just because you make the -1 smaller doesn't mean you can't do it in math.

If that were the case, every 1st grade math problem would be wrong because 1st graders make all their numbers different sizes.

You're retarded, fuck.

[Anonymous No.7259669]

>>7259516
How many groups of 1 can you make with 1?
How many groups of nothing can you make with 1?

Also, you are retarded.

[Anonymous No.7259769]

>>7259575
if death is 0 and life is 1, if we divide life by zero does that give us infinite death or infinite life

[Anonymous No.7259777]

>>7259769
*if death is 0 and life is 1e(-infinity), if we divide life by zero does that give us infinite death or infinite life

[Anonymous No.7259816]

>>7259516
Try converting them into decimals to conceptualize them.

If you have 1 of 1 parts, you have 100%, or 1 whole unit.

Is it possible to have 1 of 0 parts?

[Anonymous No.7260096]

>>7259816
yes

girlfriends

[Anonymous No.7260179]

>>7259516
Division is the process of putting a number into equal groups according to the number of the divisor.

So, 1/1 is 1 being put into groups of 1. The number of 1's in the group of 1 is 1. So, 1/1=1.

[Anonymous No.7260217]

First off, 1 split into 1 pieces result in each piece being 1. 1/1=1

For the second part look at it this way.
Take the graph of 1/x. As x gets smaller, 1/x gets much bigger.
1/0.001 =1000
1/0.000001=1000000
So, we says that 1/x approaches infinity as x approaches 0.

idk, if that makes sense...

[Anonymous No.7260221]

>>7259516
Division is just counting the number of steps it takes to get a number down to zero.

1 divided by 1 is 1-1=0

It takes 1 step for 1 to get to zero by taking away 1, so therefore 1/1=0

1/0 is a special case. Cause 1-0=1, and it'll carry onto infinity. Some people use this fact to say that 1/0 is infinity, but it's not accepted.

2/0= 2-0=2, 2-0=2, 2-0=2, and so on and so forth. Using this, I can assume that 2/0=infinity too and say that 1/0=2/0 and therefore 1=2.

[Anonymous No.7260227]

>>7260221
Lol mistake in the 3rd Line: 1/1=1

[Anonymous No.7260281]

>>7259516
>Why is 1/1 not 0?
I'll make it easy for you, OP.
Imagine that you have one apple, and you have to distribute it to 1 person. How many apples will that person get?

[Anonymous No.7260305]

>>7259516
I think of the division notation as saying "What number multiplied by the denominator yields the numerator." No number multiplied by zero yields a number other than zero, so division by zero is undefined.

[Anonymous No.7260310]

>>7259516
Math is just made up. A set of particularly useful imaginary structures, but made up. If you want to define 1/1 = 0 you can do that, but the resulting structure would be neither very useful nor very interesting.

[Anonymous No.7260334]

>>7260281
2 ?

[Anonymous No.7262256]

>>7260281
>Imagine that you have 0 apple, and you have to distribute it to 0 person. How many apples will that person get?
0 apple but 0/0 != 0

[Anonymous No.7262293]

>>7260221

what the fuck did I just read?

>division is just counting the number of steps it takes to get a number down to zero
>treating infinity as a specific value

[Anonymous No.7262295]

>>7259516
>inb4 ur a retard OP
ur a retard OP

[Anonymous No.7263551]

a/b = the x such that x*b = a

1/1 = the x such that x*1 = 1
which is 1

1/0 = the x such that x*0 = 1

x*0 = 0, which does not equal 1


unless, of course, you're working in a wheel
but you probably don't know what that means

[Anonymous No.7263558]

>>7259535
it's impossible to divide something so much that it no longer exists

[Anonymous No.7264165]

>>7263551
autist detected

[Anonymous No.7264170]

>>7260217
>calculus
git out

[Anonymous No.7264176]

>>7264165
Dumb people don't belong on /sci/.