# No, Your Favorite Product is NOT the Best

#### Neal Pert

##### Well-known member
I'm starting to think there may be a conspiracy to turn my threads into absolute mayhem. • • Stroman, C.M. Jones, Supergrobi and 1 other person

#### Supergrobi

##### Technical Supervisor
One cannot simply "eliminate" something from an equation. What happens is that you "do something" to both sides of the equation to shorten it. Example:

Code:
``````2x² - 8 = 0 | +8
2x² = 8 | :2
x² = 4 | √
x = 2``````

In this case you would have to divide by zero - which is undefined for lots of reasons.

#### MrInsanePolack

##### Platinum Member
What we do is divide one side by the common factor, which reduces it to 1
We must do this to both sides of the equation to maintain balance.

I did say you can show the work if you want. But it just basically comes down to removing the common factor from either side, or that's what the math will lead to anyhow.

It looks like this with the work: #### MrInsanePolack

##### Platinum Member
One cannot simply "eliminate" something from an equation. What happens is that you "do something" to both sides of the equation to shorten it. Example:

Code:
``````2x² - 8 = 0 | +8
2x² = 8 | :2
x² = 4 | √
x = 2``````

In this case you would have to divide by zero - which is undefined for lots of reasons.
You dont do the work inside the parentheses. Example: (X-Y-Z). You cant solve for that. Nor do you have to.

#### Al Strange

##### Well-known member
One cannot simply "eliminate" something from an equation. What happens is that you "do something" to both sides of the equation to shorten it. Example:

Code:
``````2x² - 8 = 0 | +8
2x² = 8 | :2
x² = 4 | √
x = 2``````

In this case you would have to divide by zero - which is undefined for lots of reasons.
I’ve been pondering this one all day, I wonder if you guys can help me…

Equation: σ ≤ Hn +ln (Hn)eHn
• Where n is a positive integer
• Hn is the n-th harmonic number
• σ is the sum of the positive integers divisible by n
For an instance, if n = 4 then σ(4)=1+2+4=7 and H4 = 1+1/2+1/3+1/4. Solve this equation to either prove or disprove the following inequality n≥1? Does it hold for all n≥1? • C.M. Jones

#### beatdat

##### Senior Member
We must do this to both sides of the equation to maintain balance.

I did say you can show the work if you want. But it just basically comes down to removing the common factor from either side, or that's what the math will lead to anyhow.

It looks like this with the work:
View attachment 109066
Ah, yes, you're right about doing it to both sides of the equation.

Still, I think my first post on this is relevant, in that you have to calculate the equation in the brackets first, which is why I initially said you're dividing something by 0.
You dont do the work inside the parentheses. Example: (X-Y-Z). You cant solve for that. Nor do you have to.
Why not? I thought we were supposed to?

I’ve been pondering this one all day, I wonder if you guys can help me…

Equation: σ ≤ Hn +ln (Hn)eHn
• Where n is a positive integer
• Hn is the n-th harmonic number
• σ is the sum of the positive integers divisible by n
For an instance, if n = 4 then σ(4)=1+2+4=7 and H4 = 1+1/2+1/3+1/4. Solve this equation to either prove or disprove the following inequality n≥1? Does it hold for all n≥1? Nerd.

• Al Strange

#### Supergrobi

##### Technical Supervisor
Brackets always have to be solved first.

• beatdat

#### C.M. Jones

##### Well-known member
I'm starting to think there may be a conspiracy to turn my threads into absolute mayhem. Take it as a compliment. "Absolute mayhem" threads are by far the most engaging, math notwithstanding in this case.

• • beatdat and Al Strange

#### MrInsanePolack

##### Platinum Member
Why not? I thought we were supposed to?
If the exact same function is on both sides of the equation, it's easier to just remove it. If the equation @Al Strange presented us was in the parentheses, do you wanna solve it first or just get rid of it?

Brackets always have to be solved first.
In order of operations, yes:
1+2(3+4)=x
1+2(7)=x
1+14=x
15=x

In algebra, not always:
1+2(x+y)=z

#### Supergrobi

##### Technical Supervisor
If the exact same function is on both sides of the equation, it's easier to just remove it.
Again: one cannot simply remove stuff from equations.

All this is explained quite well on wikipedia, a good starting point.

#### beatdat

##### Senior Member
If the exact same function is on both sides of the equation, it's easier to just remove it. If the equation @Al Strange presented us was in the parentheses, do you wanna solve it first or just get rid of it?

In order of operations, yes:
1+2(3+4)=x
1+2(7)=x
1+14=x
15=x

In algebra, not always:
1+2(x+y)=z

I hear you, but I don't think you can apply BEDMAS to variables (eg. algebra).

#### Stroman

##### Platinum Member
We must do this to both sides of the equation to maintain balance.

I did say you can show the work if you want. But it just basically comes down to removing the common factor from either side, or that's what the math will lead to anyhow.

It looks like this with the work:
View attachment 109066
The error in this is that you must solve the part in parentheses first, which in both cases results in an attempt to divide by zero. As has been pointed out, dividing by zero is undefined and gives us no useful information.

In layman's terms, zero times anything gives an answer of zero. If, as in the fallacy posted, we just "dropped" the zero from both sides, that would indicate that any number equals any other number, which is obviously untrue. This is one of the very reasons division by zero is undefined. I used to be a math teacher, and at one point I could show you proofs to demonstrate this, but I'm not going there now, lol.

The important thing to remember about math is that it's simply a language developed to describe natural phenomenon. If the words in a language don't mean anything, and there are no grammar rules, there's no communication.

Sorry Neal Pert, I just contributed to the mayhem, but I couldn't help it!! Last edited:

#### Al Strange

##### Well-known member
Sorry Neil Pert, I just contributed to the derailment, but I couldn't help it!! This ^^^ x10… • Stroman

#### MrInsanePolack

##### Platinum Member
Regardless of whatever it is I'm done. I'm going to confuse myself apparently even more than I already am.

#### GetAgrippa

##### Platinum Member
I choose behind curtain number two ( why no zero curtain that’s discriminatory against zero as a legit number-that’s not right). No I pick the blue pill….no red, blue.
The answer is 0.000000000. I know one thing for sure when I’m down to zero it’s time to get more zeroes. I hate running out of nil to none. Without some reminder you forget all about having none. I choose to be a hero with a lot of zero. So maybe I’m more an anti-hero but I just see that as an added dimension which is obviously lacking being the zero dimension.

• Al Strange

#### beatdat

##### Senior Member
I choose behind curtain number two ( why no zero curtain that’s discriminatory against zero as a legit number-that’s not right). No I pick the blue pill….no red, blue.
The answer is 0.000000000. I know one thing for sure when I’m down to zero it’s time to get more zeroes. I hate running out of nil to none. Without some reminder you forget all about having none. I choose to be a hero with a lot of zero. So maybe I’m more an anti-hero but I just see that as an added dimension which is obviously lacking being the zero dimension.
Have you considered a career in hip-hop?

• • Al Strange, Stroman and GetAgrippa

#### Xstr8edgtnrdrmrX

##### Well-known member
I'm starting to think there may be a conspiracy to turn my threads into absolute mayhem. Take it as a compliment. "Absolute mayhem" threads are by far the most engaging, math notwithstanding in this case.

this is one of the reasons I love this place!!!

but as soon as you guys started mixing letters with numbers, I was out...

• • C.M. Jones, Al Strange, Stroman and 1 other person

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