3=0

[Bear]

If:
x² + x + 1 = 0

Then shouldn't:

x² + x = -1

[Bear]

I think mods need to remove an irrational amount of numbers.

[Tanya]

Besides by using substitution in this way, it's logically stating x doesn't represent 1 unknown but two unknowns meaning it's better to write as.

Therefore one of the x's in the problem equals 1, not both.

n^2 + a + 1 = 0

The logical error is both x's in this equation doesn't represent the same value.

[unoduetre]

If:
x² + x + 1 = 0

Then shouldn't:

x² + x = -1

Yeah, but where is the problem?

[unoduetre]

Besides by using substitution in this way, it's logically stating x doesn't represent 1 unknown but two unknowns meaning it's better to write as.

Therefore one of the x's in the problem equals 1, not both.

n^2 + a + 1 = 0

The logical error is both x's in this equation doesn't represent the same value.

Which step is it?

[Tanya]

Obviously step 1 should be a later step above

As the first step should be assigning different variablse to represent each x first.

[unoduetre]

Oh, you mean that the x-es in the original equation represent two different values.

One is free to write any equation. There are no rules that one cannot write some equations.

(But you're close.)

[unoduetre]

OK, I will tell you what's wrong with this.

Every equation needs a set of possible solutions. Usually it's something like all real numbers (those are the usual numbers) or all complex numbers (a complex number is a sum of a real number and an imaginary number (or just a real number or just an imaginary number, so all real numbers are also complex numbers)), or some other kind of numbers. For this problem the set of possible solutions has not been specified. Now why it's important?

It's a quadratic equation (in the simplified form, the biggest power of x in this equation is 2). A quadratic equation has 0, 1 or 2 solutions in real numbers. But it has 1 or 2 solutions in complex numbers. So there is a difference.

---

If we assume this problem is to be solved in real numbers, then it's possible that this equation has no solutions. And this is exactly the case for this particular equation. There is no real number x which fulfills this equation.

So how to solve equations in a correct way? The first step one must do is one must make an assumption:

Step 0: Let's make a temporary assumption which we need to verify later that there is an x that fulfills this equation.

Apply steps 1 to 21.

We find that x = 1.

Now let's see if x really fulfills the equation by substituting x into the original equation:
1² + 1 + 1 = 3
3 ≠ 0
We get a contradiction, so our assumption in step 0 was incorrect and there are no such x.

The situation could be different for different equations.

---

If we assume this problem is to be solved in complex numbers, it's not possible that there are no solutions (It's a mathematical theorem that solutions always exist. It's called the "fundamental theorem of algebra": https://en.wikipedia.org/wiki/Fundament ... of_algebra). So in this case we don't need to assume anything and step 0 is not necessary.

But in this case step 18 is wrong. There are 3 possible solutions of x³ = 1 in complex numbers: 1, - 1/2 + i · √3/2, - 1/2 - i · √3/2. And only two of them are the solutions of the original equation. And we need to check which of them are. We can find out that 1 is not the solution, but the other two are.

[unoduetre]

And now the question is, do they teach such a basic thing in school?

Were you taught about it?

Or maybe you were only taught to blindly apply mathematical operations without really understanding what's going on and without questioning the assumptions.

I'll leave you with this question.

---

In other words, if one assumes bullshit, one gets bullshit. Garbage in, garbage out. There is a logical law which states that from a false assumption you can get ANY result.

[WorldIsMine]

And now the question is, do they teach such a basic thing in school?

Were you taught about it?

Or maybe you were only taught to blindly apply mathematical operations without really understanding what's going on and without questioning the assumptions.

I'll leave you with this question.

---

In other words, if one assumes bullshit, one gets bullshit. Garbage in, garbage out. There is a logical law which states that from a false assumption you can get ANY result.

you and i both know that critical thinking revolving around any subject in school is rarely taught

[unoduetre]

you and i both know that critical thinking revolving around any subject in school is rarely taught

Indeed.

[WorldIsMine]

i was taught critical thinking about history/social studies in high school but that's only because the teacher cared

[unoduetre]

Yeah. But beware of "critical" = postmodern.

It's like the opposite side of the coin. According to them "everything is just made of assumptions, social constructs etc. and truth and reality doesn't exist."

I hope in the case of that history teacher it was actually critical and not "critical".

[WorldIsMine]

i mean i came out critical of the US government for the horrible, horrible, horrible shit we've done so it was mostly about contrary points

[unoduetre]

OK