step 4, it is illegal to divide by 8-8 because 8-8 equal zero

In step 4, dividing by 8-8 means dividing by zero. This is not allowed, so the answer is step 4 .

0 cannot be a denominator therefore cannot decide by 8-8

You can neither divide by 0 or multiply by 0 in order to simplify, here is why:

(just for understanding) 2 = 1 (i know this is false but will get there later) because we are technically allowed to multiply with 0 -> 0 x 2 = 0 and 0 x 1 = 0

so ... technically its possible but if we wanna simplify we get this:

2 = 1 | x 0

0 = 0 q.e.d. (Quo errat demonstrator) obviously doesnt work ... so we are not allowed to devide and multiply by 0 to simplify ... that does not mean we are not allowed to divide or multiply by 0 at all. I say $\frac{0}{0}$ = {-∞;...;∞} So here we go!

0 x 9 = 0

0 x 32423,23423 = 0

0 x 0,00001 = 0

so 0/9 = 0 ... and now comes the problem 0/0 = 9 is not correct ... it is just partly correct, because it is one solution out of many!

0/0,00001 = 1 ... same thing 0/0 = 0,00001 is not correct ... it is just a part of the solution.

now this messes with a few rules... but not entirely

for example: every number divide by itself is 1 -> $\frac{a}{a}$ = 1 but now we have to make an exception a ∈ Q and a ≠ 0 (because we cannot divide by 0 for this rule)

ok now partly it is actually correct 0/0 can be 1 because 0 x 1 = 0 but it cannot ONLY be 1 thats why we cannot say 0/0 = 1

making it simple now: every number (a) multiplied with 0 equals 0 -> logically 0/0 equals every number (a)

example: I have 0 pieces of cake and I invite (a) number of people, then everyone will get 0 pieces (0 x a = 0) it doesn't matter how many people will come

now i divide by 0: (0/0 = a): I have 0 pieces of cake and the rule that everyone that got invited and came will get 0 pieces of cake -> I don't know how many people will come but it actually doesn't matter how many people will come.

and now it is clear why you cannot divide by 0 in order to simplify -> it just adds an infinite ammount of solutions to both sides (in case you divide 0 by 0)

and multiply with 0 would make it 0 solutions

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now this is maybe hard to understand and I think the reason is the "=" equal symbol so let me try to explain:

4/2 = 2/1 mathematically this is correct but it doesn not really look equal does it?

2 = 2 simplified it looks better right?

√4 = 2 this is also just a part -> just like 0/0 = 1

√4 = {2; -2} and now look at this! -> 0/0 = {-∞;...;∞}

we have to define what we want -> √4 = b and (b ∈ N) then b = 2 but if (b ∈ Z) then b = {2; -2}

now for my cake example: '0' cakes 'x' (multiplied) with 'a' ammount of people '=' "equals" '0' pieces for each person -> a ∈ N because there are no negative people or half ones and lets say i know 100 people then a < 101

in this specific case 0/0 = {0;1;2;...;98;99;100} because I know how many pieces I have and how many pieces everyone will get but I stil don't know how many people will come ... it is actually irrelevant

and last but not least for x/0 and x ≠ 0... this just doesn't exist ... we can imagine it but it simply doesn't exist

it is like a unicorn ... we can't say 100% there is no unicorn (because who knows) but ... if someone asked us if unicorns exist we would tell them "no they don't"

a lot of people can tell you a lot of things ... some say there is a god but others won't believe and we can't prove them wrong ( we cannot prove that 3/0 doesn't exist)

I say in order for things to exist, you need to prove existence with definition and logic... well this is what I believe but maybe im wrong

step 4 has flawed logic, as when working with algebra, ALL TERMS must be divided by the same thing, not just each side for example: 7-7=8-8 $\frac{7}{8-8}$ - $\frac{7}{8-8}$ = $\frac{8}{8-8}$ - $\frac{8}{8-8}$ which works out as $\frac{7}{0}$ - $\frac{7}{0}$ = $\frac{8}{0}$ - $\frac{8}{0}$ and as it has been mathematically proven, this is impossible and BADMAS states that multiplication is solved before subtraction, unless brackets state otherwise so $\frac{7-7}{8-8}$ equals 0/0 which is impossible and always ALWAYS explain where numbers come from, like that one for example. why did you chose 1? why not ten? or zero? if you're going to take a number out of context, the entire equation is invalid

thus proving this whole thing false

$\frac{8-8}{8-8}$ is equal to $\frac{0}{0}$ , not 1. If it was = 1, that would be using the conjecture you are trying to prove in the proof for that conjecture, which doesn't make any sense. So, essentially, this proof comes out to $\frac{0}{0}$ = $\frac{0}{0}$ , which I suppose is technically true even though both terms are undefined.

Dividing by zero is an illegal action and results in an undefined number tending to infinity - a singularity. Dividing by 8-8 means you are dividing by zero thus the solution is flawed. This concept gives rise to various anomalies in mathematics making things seem something the are not and can be rather quirky. Beware of dividing by zero - try it on your calculator for instance. There are philosophical arguments around this property of zero.

Step 4: "Dividing both sides by 8-8" (8-8=0).
Divide by zero is not allowed. By using divide by zero we got the wrong result.

The answer is Step 4 because 7-7=8-8 and (7-7)/(8-8) is not the same. Proof: 7-7=8-8 equals 0=0 but 0/0 equals any number. I can explain why 0/0 equals any numbers. Prove: if 0/0 is 0, it satisfies 0=0 0 Then 0/0 is 1, it satisfies 0=0 1 And 0/0 is 2, it satisfies 0=0*2 So there are so many answers of 0/0, I explained why 0/0's solution is any numbers. 0/0=x(x is not 0), any value of x satisfies in natural number, integer, rational number, an irrational number, real number, imaginary number, complex number.

because of the priority of operations (7-7)x(8-8)^-1 we're supposed to apply the substraction first wich lead us again to 0/0

8-8 equal 0. Deviding by zero is undeterminated, it will be demonstrate.

8 does not equal 7, and only equal numbers will cancel out to create 1, so step 4 is incorrect.

From step 3 to step 4: You said to divide both side by 8-8, so it would represent as $\frac{7-7}{8-8}$ = $\frac{8-8}{8-8}$ . But you considered LHS=1 ------> i.e., $\frac{0}{0}$ which you are still proving it as 1. You can't take it as 1. This was the error. Thank You.

0/0=any number since we can't divide normally we can do reverse multiplication so ?x0=0 since anything multiplied by 0=0 in this equation ?=any number which means 0/0=any number

$\frac{(8-8)}{(8-8)}$ = $\frac{0}{0}$ also $\frac{(7-7)}{(8-8)}$ = $\frac{0}{0}$ Therefore, all we can say is that: $\frac{0}{0}$ = $\frac{0}{0}$

there is no variable that allow an operation can make this problem divide, in another words the variable need to appear in the operation if you want to realize an operation such as multiplication, division, or radication.

Step 4 is: $\frac{7-7}{8-8}$ = $\frac{8-8}{8-8}$ . As we already know, 7-7=0 and 8-8=0...... Therefore: $\frac{7-7}{8-8}$ = 0 and $\frac{8-8}{8-8}$ = 0.... So the equation becomes: $\frac{0}{0}$ = $\frac{0}{0}$ .... So $\frac{0}{0}$ does not equal 1 - it equals itself according to this set of equations, and thus, step 4 was incorrect. Step 4 assumes that $\frac{8-8}{8-8}$ is equal to 1, when in fact, it is equal to $\frac{0}{0}$ which has not yet been proven to be 1. Hope this makes sense :)

• Simply because (7-7):(8-8)=(7-7):0 which you're not allowed to

From "algorithmic POW" step 4 essentially means "go back to step 1", or create subroutine containing "step 1 to 4", which leads to creating subroutine containing "step 1 to 4", which leads to creating subroutine containing "step 1 to 4", which leads to creating subroutine containing "step 1 to 4"... Poor CPU. As for why 0/0 is sometimes defined as 1 is pratical reasons. Unexpected operations with "1" are not likely to lead to a catastrophe. Unexpected operations with "0" invariably do.

when you divide the both side of the equation by 8-8, you are assuming that the right side is equal to 1, but 8-8 (zero) divided by 8-8 (zero) is not equal to 1, it is an indeterminacy.

I just guessed

8-8 equals 0.

As a student of calculus at a university, i say that a division by zero egual= indefinition.

step 4. 7-7/8-8 = 0/0 is illegal. this explaination is more like a magic trick designed to lure humans more than math

$\frac{8-8}{8-8}$ evaluates to $\frac{0}{0}$ but we can't just skip that fact and go straight to 1 because that's exactly what we're trying to prove.

0/0 is 1 because 0/0=0^1/0^1=0^0=1

Where zero = 0, logic cannot be made, but where 0 = zero or 0, logic can be assumed because zero and naught are not necessarily the same nor equal.

In Step 4 you divide by Zero, and its not defined

Step 4, he divided 0 by 0 and got 1 to prove that when you divide 0 by 0 you get 1... circular argument lol

As we divide 8-8\8-8 , so in the denominator we will get 0 as an answer . Therefore, any number divided by 0 will be infinity.

Dividing 8-8 by 8-8 does not give 1

step 4 8-8 is 0 dividing by 0 = $\pm \infty$ which is impossible

Let's check every steps ,

Step:1 We can rewrite $15$ as $7 + 8$ or (8 + 7)

Since $7 + 8 = 15$ or $8 + 7 = 15$ so step 1 is correct.

Step 2: This means that $7 + 8 = 8 + 7$

$15 = 15$ so step 2 is correct.

Step 3: If we move one term from each side of the equation to the other side, we will get $7 - 7 = 8 - 8$

Step 3 is correct

Step 4: Dividing from both sides by $8 - 8$ gives $\dfrac{7-7}{8-8} = 1$

$\dfrac{7-7}{8-8} = \dfrac{0}{0}$ and division by 0 is not allowed , therefore $\boxed{\text{step 4}}$ is incorrect.