Confused about this "equation" I heard from someone

[Zantos]

I was playing a game on a server. Well, minecraft. Well someone was doing a math test. Whoever won got a prize. He said the higher the level the more money you get. Well level 1 was easy. 9x9. Then his level 2 question. He said, What does a x b =. With the x meaning the same as in 9 x 9. Now, I was confused because I was thinking there would be something like Solve for b or he would give some meaning behind the numbers. However, he gave nothing else to it. So I answered C, just something I heard someone in a show or something. No one got it right and he said the answer to a x b was ab. Now, I am from the US. In everything I was taught those are the same equation with the same meaning. Meaning to multiple a by b. So I proceeded to ask him but he couldn't explain being that he was apparently dutch and not very good at english.

So I ask this to anyone who's good at math. When they say what does a x b =, why would it equal literally itself? Why would it equal the same equation? I would assume that if they meant to get ab from it they would say give a different way to solve a x b. Now this is going from what my school district taught which, by what I saw, was pretty low from literally every other surrounding district.

[Deleted]

a x b = ab

ab is the same thing as a x b, in equations you usually don't put a multiplication sign between letters.

[Zantos]

a x b = ab

ab is the same thing as a x b, in equations you usually don't put a multiplication sign between letters.

Yeah, because you might confuse x as one of the letters. But why does a x b = ab if the only thing someone states is what does a x b =? If they were looking for ab shouldn't they specifically say list another way to write the formula a x b? Or is this one of those small, defy common sense type deals that they teach in school?

[Waaldo]

When 2 letters are next to each other it means multiplication, and basically that equation is an example equation that you would see at the beginning of a chapter about multiplication/algebra. So a and b have no meaning, it is just to show you that a x b is the same as ab. When there are multiple variables you are supposed to simplify it, and when the equation is already very simple, not much changes. But if you had a x b x (2+4) the simplified equation would be 6ba, so when you do get the variables (a=5 for example) you can plug them in with the least amount of work to be done, because the equation was already as close to finishing as possible.

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Yeah, because you might confuse x as one of the letters. But why does a x b = ab if the only thing someone states is what does a x b =? If they were looking for ab shouldn't they specifically say list another way to write the formula a x b? Or is this one of those small, defy common sense type deals that they teach in school?

Yes, it's referred to as algebra, and pretty much everyone hates it.

[Zantos]

When 2 letters are next to each other it means multiplication, and basically that equation is an example equation that you would see at the beginning of a chapter about multiplication/algebra. So a and b have no meaning, it is just to show you that a x b is the same as ab. When there are multiple variables you are supposed to simplify it, and when the equation is already very simple, not much changes. But if you had a x b x (2+4) the simplified equation would be 6ba, so when you do get the variables (a=5 for example) you can plug them in with the least amount of work to be done, because the equation was already as close to finishing as possible.

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Yes, it's referred to as algebra, and pretty much everyone hates it.

I think I remember that chapter now. To simply put, when they list a x b = they are essentially saying with = to put the equation in its simplest form. I can see how that could easily be forgotten from high school. That was in my junior year so 5 years.

[Saphyron]

Algebra is not that bad.

It just confuses people. Like the exam I just had where I need to isolate r in this formula K = k * (1 + r)^n

Its fun. At least for me.

[Deleted]

Yeah, because you might confuse x as one of the letters. But why does a x b = ab if the only thing someone states is what does a x b =? If they were looking for ab shouldn't they specifically say list another way to write the formula a x b? Or is this one of those small, defy common sense type deals that they teach in school?

Mathematicians are just lazy... there's really nothing else to it.

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Algebra is not that bad.

It just confuses people. Like the exam I just had where I need to isolate r in this formula K = k * (1 + r)^n

Its fun. At least for me.

I love algebra too.

[Deleted]

Feel like this question has already been answered but yeh, its just the way algebra works. You tend to put equations into their simplest form.

ab is a more simple form of a x b

When you work/study with algebra you come across equations that are so large it would just seem ridiculous to repeat sign and add additional characters/symbols when you could just leave them without and compress the whole thing.

[Hyve]

I understand why we don't say a x b = c, as x could easily be confused as part of the calculation, potentially resulting in people looking for axb.

Why though in 2014 we've not mastered the use of this little guy; *, I don't know.

A * B = C is easily understood, as is A / B, A + B, or A - B.

[Deleted]

as x could easily be confused as part of the calculation, potentially resulting in people looking for axb.

I genuinely don't think this has much to do with it. In written algebra x isn't drawn with two straight lines. It's just we can compress the equation by getting rid of the multiplication symbol.

I do agree that it's strange we don't use * / etc in written mathematics, given they're the symbols we use to make calculations on computers. But meh, it's not asif its difficult to work with either written method.

[Bepples]

a x b = ab

ab is the same thing as a x b, in equations you usually don't put a multiplication sign between letters.

Unless a and b are vectors and you are doing a cross product, in which case:
a x b = (a₂b₃ - a₃b₂)i + (a₃b₁ - a₁b₃)j + (a₁b₂ - a₂b₁)k

Algebra is not that bad.

It just confuses people. Like the exam I just had where I need to isolate r in this formula K = k * (1 + r)^n

Its fun. At least for me.

r = e^[log(K/k)]/n - 1

?

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I understand why we don't say a x b = c, as x could easily be confused as part of the calculation, potentially resulting in people looking for axb.

Why though in 2014 we've not mastered the use of this little guy; *, I don't know.

A * B = C is easily understood, as is A / B, A + B, or A - B.

AB is easy enough to understand because multiplication essentially combines two expressions into one in a commutative way (i.e. ab = ba). Some equations would start to look pretty ridiculous with the unnecessary use of '*'. For example, the cross product formula:

a x b = (a₂b₃ - a₃b₂)i + (a₃b₁ - a₁b₃)j + (a₁b₂ - a₂b₁)k

becomes:

a x b = (a₂*b₃ - a₃*b₂)*i + (a₃*b₁ - a₁*b₃)*j + (a₁*b₂ - a₂*b₁)*k

It looks a lot messier for no real reason. It hasn't become easier to understand at all.

[Saphyron]

r = e^[log(K/k)]/n - 1

?

Have never seen it written like that before

K = k * (1 + r)^n
K/k = (1 + r)^n
n-root(K/k) = (1 + r)
n-root(K/k) = 1 + r
n-root(K/k) - 1 = r

or



This formula is to calculate the interest of interest
K = end number
k = start number
r = interest
n = duration

Sorry not english, im danish so don't know what they are specificaly called in english.

[Bepples]

Yeah, because you might confuse x as one of the letters. But why does a x b = ab if the only thing someone states is what does a x b =? If they were looking for ab shouldn't they specifically say list another way to write the formula a x b? Or is this one of those small, defy common sense type deals that they teach in school?

In this situation a and b are both unknown numbers; we use letters for that exact reason. That's pretty much all algebra is: using letters to represent patterns involving unknown numbers. You don't know what a and b are so the only thing you can say with confidence about the equation a x b is that the answer is ab: the product of a and b. Yeah, it sounds like just the same thing repeated, but that really is the answer.

All a x b = ab is saying is that "if you multiply a by b, you get the product of a and b". Sure, you can say "if you multiply a by b, you get c", but that's even more pointless because c will just be equal to ab. So you are just introducing an extra letter that does nothing but complicates things. None of it really defies common sense and it is taught in school for a very good reason.

[Asetotti]

Have never seen it written like that before

K = k * (1 + r)^n
K/k = (1 + r)^n
n-root(K/k) = (1 + r)
n-root(K/k) = 1 + r
n-root(K/k) - 1 = r

or

[IMG]http://i.imgur.com/mKcZXt1.jpg[IMG]

Who the fuck uses "n-root".. Logarithms all the way.
Note that both


(n≠0 and k≠0
nvm ninja edit)

[Bepples]

Have never seen it written like that before

K = k * (1 + r)^n
K/k = (1 + r)^n
n-root(K/k) = (1 + r)
n-root(K/k) = 1 + r
n-root(K/k) - 1 = r

or

Ah, I see. This is how I went with it:



I guess I just overcomplicated things. They really are the same thing though, as different as they look XD

The logarithm approach is just really helpful when doing series calculations.

(also, assume every time I say "log" I am using a logarithm with the base "e").

[Wikiy]

I guess I just overcomplicated things. They really are the same thing though, as different as they look XD

The logarithm approach is just really helpful when doing series calculations.

(also, assume every time I say "log" I am using a logarithm with the base "e").

So you're using "log" as "ln"? I guess that's fine, but I don't get the point in using logarithms here in general. Why use it when you get a number with a base e and exponent which has ln in it? A number which is, honestly, sort of uselessly incomprehensible and confusing. I prefer n-root(K/k) much more over e^((ln(K/k))/n).

[nextormento]

I understand why we don't say a x b = c, as x could easily be confused as part of the calculation, potentially resulting in people looking for axb.

Why though in 2014 we've not mastered the use of this little guy; *, I don't know.

A * B = C is easily understood, as is A / B, A + B, or A - B.

Because while we use the cross sign when learning arithmetic:
3 × 4 = 12
there's plenty of people that denote multiplication as a dot when starting algebra, so we have perfectly fine symbols without using asterisks:
2 ⋅ x
I must add that my teachers made a big case for not confusing 'x' with '×': they're two different characters. And they made us write our 'x' in sufficiently sophisticated ways as to not be confused.

Now, when we normally speak we say 'three times four' and it sounds good. But 'two times apples' does not: we say 'two apples'. Thus, we omit the sign:
2x

No sign, no confusion, no complexity. The asterisk is only used in computer science, and there it still has a wide variety of meanings (such as a wild card character). I think asterisks would add a whole lot of complexity for no good reason.

[Cyberowl]

Some people like hot wax being poured on their testicles, some people like algebra. Hey, who am I to judge? Live and let live!

I wish I was still good at math, but unfortunately my teacher in the last 3 years was like the worst and my motivation wasn't high enough to teach myself all the stuff I was missing in his lessons. At least I didn't take math in my final exams, 2/3 of my class failed the math test and the teacher was sent into pension after it (did I say he was shit already?).

But yeah, a x b = ab is pretty basic, one should know that!

[Bepples]

So you're using "log" as "ln"? I guess that's fine, but I don't get the point in using logarithms here in general. Why use it when you get a number with a base e and exponent which has ln in it? A number which is, honestly, sort of uselessly incomprehensible and confusing. I prefer n-root(K/k) much more over e^((ln(K/k))/n).

Some problems require the logarithm method. For example, if you needed to find n in that equation, you NEED to use logarithms. This might sound like an exotic problem, but it is very common when doing series calculations.

For example. I have the following infinite series:

1 + 2 + 4 + 8 + 16 + 32 + 64 + ...

The starting number is "1", ratio of each term and the term preceding it is 2 (every term is double the last). The equation to describe any given term in this series is:

T_n = ar^n-1

a is the starting number (1) and r is the ratio (2). If I wanted to find the fifth term, I would substitute "5" for "n":

T₅ = 1*2^5-1
T₅ = 16

That makes sense, it matches the pattern. Now what if I wanted to find the first term which is greater than 2000?

T_n > 2000
2^n-1 > 2000

Sure, you could randomly test values of n until you find it, or you could try to solve for n directly.


Testing n=12:
T₁₂ = 2¹¹
T₁₂ = 2048

So it makes sense.

To solve for n here, you MUST use logarithms. Otherwise, you guess and check the values for n. This might be easy for this series, but not all series are this simple.

So I guess in the problem he linked, since he just had to isolate r the n-root approach is more simple and very valid. But you will eventually encounter logarithms, so you do need to know that stuff as well. They aren't just exotic numbers you can ignore; they have practical purpose.

[Hyve]

AB is easy enough to understand because multiplication essentially combines two expressions into one in a commutative way (i.e. ab = ba). Some equations would start to look pretty ridiculous with the unnecessary use of '*'. For example, the cross product formula:

a x b = (a₂b₃ - a₃b₂)i + (a₃b₁ - a₁b₃)j + (a₁b₂ - a₂b₁)k

becomes:

a x b = (a₂*b₃ - a₃*b₂)*i + (a₃*b₁ - a₁*b₃)*j + (a₁*b₂ - a₂*b₁)*k


It looks a lot messier for no real reason. It hasn't become easier to understand at all.

Personally, the bottom looks nicer to be. Maybe I'm weird like that.