7.0% actually 3.69%?

zagfles

AmityNeon said:

zagfles said:

AmityNeon said:

zagfles said:

Not sure about only logic, you do need a bit of arithmetric training. Rearranging an equation is usually as hard or harder than "simplifying", and you can't use a (normal) calculator for that, and you do need to rearrange when the value you're resolving for is on both sides of the equation. 

Basic rearranging only requires an elementary understanding of arithmetic, and the rest is logic; if an operation is performed on one side of an equation, it must also be performed on the other for logical consistency.

It's not mostly logic though. Perform the "same operation" on both sides? Very logical. But you need to understand that you need to perform the same operation on every element if it's a multiplication, but not if it's addition etc.

eg a + b = c

ax + bx = cx (every element multiplied by x)

But

a + b + x = c + x (not a+x + b+x = c+x)

The fundamentals of arithmetic are derived through the application of logic. It is not logical to add x twice on the left, but only once on the right.

Multiplication is derived from applying logic:

• x * (a + b) =
• x 'lots' of (a + b) =
• adding (a + b) to itself x number of times =
• ax + bx

These are not 'rules' a person has to learn from an external source; they can be intuitively deduced through logic, although the notation must be learnt so that the concepts can be effectively represented and communicated. As an extreme example, child prodigies are truly and naturally fascinating, not because they are born possessing a fountain of knowledge, but because of their neurological affinity and acuity.

zagfles said:

Just that the "logic" of doing the same thing to each side/each element isn't always right.

That's not mathematically logical; artistically consistent perhaps, but I wouldn't call it logic, because those symbols denote specific concepts derived from logic.

zagfles said:

Using "logic" you can actually prove that 1 = 2

xy = xz

Therefore y = z (same operation both sides, right?)

What if x is 0, y is 1, and z is 2.

xy = xz is true, both sides 0.

But logic above says that means y = z

so 1 = 2

y = z cannot be logically deduced from xy = xz if x = 0.

x being 0 means it logically nullifies anything y or z could represent, regardless of their individual values. Also, logically, you cannot split (divide) something by (or into) nothing.

We're probably entering the realms of extreme pedantry here which will futher annoy all those who are avidly reading this thread yet want it closed...but what you consider rules of logic I consider rules of maths. You said earlier it's "logical" that operations are performed on both sides give logical consistency. Multiplying/dividing by 0 is an operation. It's the rules of maths that says dividing both sides by the same value gives a consistent equation, except where that special mathematical concept of zero is involved.

There are other examples. Eg

x^2 = y^2.

So logically, x = y, right? Same operation both sides?

But x might be 2 and y might be -2. It's the rules of maths, not logic, that tell you that x = y might be incorrect if x^2 = y^2

Band7

Martin Lewis is today running a poll about financial literacy. Whilst it won't be a statistically valid result for the UK as a whole, the results are interesting.




And the results as they stand at the moment on Facebook (not sure which other platforms he is asking, too. Twitter, probably):

eskbanker

Band7 said:

Martin Lewis is today running a poll about financial literacy. Whilst it won't be a statistically valid result for the UK as a whole, the results are interesting.

And the results as they stand at the moment on Facebook (not sure which other platforms he is asking, too. Twitter, probably):

To be fair, that's probably as much a test of comprehension and reading skills as it's one of financial literacy as such!

zagfles

Band7 said:

Martin Lewis is today running a poll about financial literacy. Whilst it won't be a statistically valid result for the UK as a whole, the results are interesting.




And the results as they stand at the moment on Facebook (not sure which other platforms he is asking, too. Twitter, probably):

So 97% got it right on FB! A fairly simple question but even so, I'm impressed!

I suspect it'll be less on Tw*tter, it was probably too long a post for them

AmityNeon

zagfles said:

AmityNeon said:

zagfles said:

AmityNeon said:

zagfles said:

Not sure about only logic, you do need a bit of arithmetric training. Rearranging an equation is usually as hard or harder than "simplifying", and you can't use a (normal) calculator for that, and you do need to rearrange when the value you're resolving for is on both sides of the equation. 

Basic rearranging only requires an elementary understanding of arithmetic, and the rest is logic; if an operation is performed on one side of an equation, it must also be performed on the other for logical consistency.

It's not mostly logic though. Perform the "same operation" on both sides? Very logical. But you need to understand that you need to perform the same operation on every element if it's a multiplication, but not if it's addition etc.

eg a + b = c

ax + bx = cx (every element multiplied by x)

But

a + b + x = c + x (not a+x + b+x = c+x)

The fundamentals of arithmetic are derived through the application of logic. It is not logical to add x twice on the left, but only once on the right.

Multiplication is derived from applying logic:

• x * (a + b) =
• x 'lots' of (a + b) =
• adding (a + b) to itself x number of times =
• ax + bx

These are not 'rules' a person has to learn from an external source; they can be intuitively deduced through logic, although the notation must be learnt so that the concepts can be effectively represented and communicated. As an extreme example, child prodigies are truly and naturally fascinating, not because they are born possessing a fountain of knowledge, but because of their neurological affinity and acuity.

zagfles said:

Just that the "logic" of doing the same thing to each side/each element isn't always right.

That's not mathematically logical; artistically consistent perhaps, but I wouldn't call it logic, because those symbols denote specific concepts derived from logic.

zagfles said:

Using "logic" you can actually prove that 1 = 2

xy = xz

Therefore y = z (same operation both sides, right?)

What if x is 0, y is 1, and z is 2.

xy = xz is true, both sides 0.

But logic above says that means y = z

so 1 = 2

y = z cannot be logically deduced from xy = xz if x = 0.

x being 0 means it logically nullifies anything y or z could represent, regardless of their individual values. Also, logically, you cannot split (divide) something by (or into) nothing.

We're probably entering the realms of extreme pedantry here which will futher annoy all those who are avidly reading this thread yet want it closed...but what you consider rules of logic I consider rules of maths. You said earlier it's "logical" that operations are performed on both sides give logical consistency. Multiplying/dividing by 0 is an operation. It's the rules of maths that says dividing both sides by the same value gives a consistent equation, except where that special mathematical concept of zero is involved.

Are you saying it's not logical for that to be the case? Is it only 'mathematically correct' because the rules of mathematics say so? Do you think such rules are derived from logic, arbitrarily, biology, the scientific method, or ethics and philosophy?

I'm not saying logic alone without education can address all manner of mathematical problems, but in terms of consumer finance, it's discouraging to others if they feel they need to be 'learned' in maths when basic arithmetic and logic are all that are necessary. People don't have to like something to be able to do it, but it's in their (and everyone's) best interests to think logically and critically, and they should feel confident they can do so in all areas of life instead of believing they're just no good at maths and switching off because they haven't learned or remembered the 'rules of maths'. I only have a GCSE in maths myself, and I'm certainly not academically gifted.

dcs34

zagfles said:

Malthusian said:

zagfles said:

But you do get calculators telling you 1 + 2 x 3 = 9 when the correct answer is 7. Try the Windows calculator in standard mode, then try it in scientific mode.

Anyone with a C in IT will tell you that you asked the calculator what (1 + 2) x 3 is and it answered correctly. Not the computer's fault that your input wasn't the same as the question you wanted to ask.
You don't need to be Einstein to understand that the "standard mode" executes each operation as it goes along.

No, I asked 1 + 2 x 3. I used no brackets in my question.

The correct answer to the question I asked is 7. I asked both calculators the exact same question and got different answers. Anyone with a C in both IT and maths will tell you that the IT is rubbish as it doesn't understand the rules of maths. The answer to a simple sum like 1+2x3 isn't "well it depends if you're a scientist or not"

If you used the Microsoft Calculator on Standard Mode then you never actually asked it to compute 1 + 2 x 3. In standard mode it can only perform a single operation on each calculation line.

You asked it 1 + 2, which is immediately told you was 3 (correct).

You then multiplied that result (3) x 3, which it told you was 9 (correct).

You can argue it as a UI error, or a user error, but the actual maths was correct.

AmityNeon

zagfles said:

There are other examples. Eg

x^2 = y^2.

So logically, x = y, right? Same operation both sides?

No, because the concept of a double negative is still logical. If I owe three people a negative debt of £3 each, it equally means three people each owe me £3. I can go up uphill forwards, or turn my body around and walk backwards (whilst still moving uphill).

zagfles

AmityNeon said:

zagfles said:

AmityNeon said:

zagfles said:

AmityNeon said:

zagfles said:

Not sure about only logic, you do need a bit of arithmetric training. Rearranging an equation is usually as hard or harder than "simplifying", and you can't use a (normal) calculator for that, and you do need to rearrange when the value you're resolving for is on both sides of the equation. 

Basic rearranging only requires an elementary understanding of arithmetic, and the rest is logic; if an operation is performed on one side of an equation, it must also be performed on the other for logical consistency.

It's not mostly logic though. Perform the "same operation" on both sides? Very logical. But you need to understand that you need to perform the same operation on every element if it's a multiplication, but not if it's addition etc.

eg a + b = c

ax + bx = cx (every element multiplied by x)

But

a + b + x = c + x (not a+x + b+x = c+x)

The fundamentals of arithmetic are derived through the application of logic. It is not logical to add x twice on the left, but only once on the right.

Multiplication is derived from applying logic:

• x * (a + b) =
• x 'lots' of (a + b) =
• adding (a + b) to itself x number of times =
• ax + bx

These are not 'rules' a person has to learn from an external source; they can be intuitively deduced through logic, although the notation must be learnt so that the concepts can be effectively represented and communicated. As an extreme example, child prodigies are truly and naturally fascinating, not because they are born possessing a fountain of knowledge, but because of their neurological affinity and acuity.

zagfles said:

Just that the "logic" of doing the same thing to each side/each element isn't always right.

That's not mathematically logical; artistically consistent perhaps, but I wouldn't call it logic, because those symbols denote specific concepts derived from logic.

zagfles said:

Using "logic" you can actually prove that 1 = 2

xy = xz

Therefore y = z (same operation both sides, right?)

What if x is 0, y is 1, and z is 2.

xy = xz is true, both sides 0.

But logic above says that means y = z

so 1 = 2

y = z cannot be logically deduced from xy = xz if x = 0.

x being 0 means it logically nullifies anything y or z could represent, regardless of their individual values. Also, logically, you cannot split (divide) something by (or into) nothing.

We're probably entering the realms of extreme pedantry here which will futher annoy all those who are avidly reading this thread yet want it closed...but what you consider rules of logic I consider rules of maths. You said earlier it's "logical" that operations are performed on both sides give logical consistency. Multiplying/dividing by 0 is an operation. It's the rules of maths that says dividing both sides by the same value gives a consistent equation, except where that special mathematical concept of zero is involved.

Are you saying it's not logical for that to be the case? Is it only 'mathematically correct' because the rules of mathematics say so? Do you think such rules are derived from logic, arbitrarily, biology, the scientific method, or ethics and philosophy?

I'm not saying logic alone without education can address all manner of mathematical problems, but in terms of consumer finance, it's discouraging to others if they feel they need to be 'learned' in maths when basic arithmetic and logic are all that are necessary. People don't have to like something to be able to do it, but it's in their (and everyone's) best interests to think logically and critically, and they should feel confident they can do so in all areas of life instead of believing they're just no good at maths and switching off because they haven't learned or remembered the 'rules of maths'. I only have a GCSE in maths myself, and I'm certainly not academically gifted.

It's the opposite IMO. If people are told they should be able to solve everyday maths problems just applying inate logic, but they can't, that will discourage them. They're told they should be able to do something without being taught how and if they can't they're illogical.

If you show them rules and techniques to solve problems, then they can use them next time. It's no different to teaching children how to add up. Start at the right, add the digits, if it's over 10 carry one etc. Some people may be able to work out how to add or multiply two numbers inately, but most will use techniques and rules they were taught at school.

Same for more advanced stuff, like compound interest, mortgage repayments, algebra etc. They don't need to "remember" rules, they can look them up. But if they use them regularly the main rules will stick.

I can't remember the mortgage repayment forumla, or the arithmetric/geometric progression formulae, both useful for personal finance. If I needed them I'll look them up rather than working them out from first principles or "logic".

Bridlington1

AmityNeon said:

zagfles said:

There are other examples. Eg

x^2 = y^2.

So logically, x = y, right? Same operation both sides?

No, because the concept of a double negative is still logical. If I owe three people a negative debt of £3 each, it equally means three people each owe me £3. I go up uphill forwards, or turn around and walk backwards (still moving uphill).

But up until relatively recently the concept of negative numbers was seen as illogical. If you go back even to the early to mid 19th century it was common practice to ignore negative results derived from equations on the assumption that they were meaningless. The logic was that negative numbers can't exist physically in the real world, i.e. you can't have -3 apples, or -3 pound coins.

What is logical is a largely subjective question since it's mostly about perception. If you don't understand a concept you will likely see it as illogical just as countless mathematicians in bygone eras saw negative numbers as illogical. At the time they couldn't understand them physically so they viewed them as illogical.

Something only really becomes logical to you if you understand it, if you don't understand it it probably won't seem all that logical.

AmityNeon

zagfles said:

AmityNeon said:

zagfles said:

AmityNeon said:

zagfles said:

AmityNeon said:

zagfles said:

Not sure about only logic, you do need a bit of arithmetric training. Rearranging an equation is usually as hard or harder than "simplifying", and you can't use a (normal) calculator for that, and you do need to rearrange when the value you're resolving for is on both sides of the equation. 

Basic rearranging only requires an elementary understanding of arithmetic, and the rest is logic; if an operation is performed on one side of an equation, it must also be performed on the other for logical consistency.

It's not mostly logic though. Perform the "same operation" on both sides? Very logical. But you need to understand that you need to perform the same operation on every element if it's a multiplication, but not if it's addition etc.

eg a + b = c

ax + bx = cx (every element multiplied by x)

But

a + b + x = c + x (not a+x + b+x = c+x)

The fundamentals of arithmetic are derived through the application of logic. It is not logical to add x twice on the left, but only once on the right.

Multiplication is derived from applying logic:

• x * (a + b) =
• x 'lots' of (a + b) =
• adding (a + b) to itself x number of times =
• ax + bx

These are not 'rules' a person has to learn from an external source; they can be intuitively deduced through logic, although the notation must be learnt so that the concepts can be effectively represented and communicated. As an extreme example, child prodigies are truly and naturally fascinating, not because they are born possessing a fountain of knowledge, but because of their neurological affinity and acuity.

zagfles said:

Just that the "logic" of doing the same thing to each side/each element isn't always right.

That's not mathematically logical; artistically consistent perhaps, but I wouldn't call it logic, because those symbols denote specific concepts derived from logic.

zagfles said:

Using "logic" you can actually prove that 1 = 2

xy = xz

Therefore y = z (same operation both sides, right?)

What if x is 0, y is 1, and z is 2.

xy = xz is true, both sides 0.

But logic above says that means y = z

so 1 = 2

y = z cannot be logically deduced from xy = xz if x = 0.

x being 0 means it logically nullifies anything y or z could represent, regardless of their individual values. Also, logically, you cannot split (divide) something by (or into) nothing.

We're probably entering the realms of extreme pedantry here which will futher annoy all those who are avidly reading this thread yet want it closed...but what you consider rules of logic I consider rules of maths. You said earlier it's "logical" that operations are performed on both sides give logical consistency. Multiplying/dividing by 0 is an operation. It's the rules of maths that says dividing both sides by the same value gives a consistent equation, except where that special mathematical concept of zero is involved.

Are you saying it's not logical for that to be the case? Is it only 'mathematically correct' because the rules of mathematics say so? Do you think such rules are derived from logic, arbitrarily, biology, the scientific method, or ethics and philosophy?

I'm not saying logic alone without education can address all manner of mathematical problems, but in terms of consumer finance, it's discouraging to others if they feel they need to be 'learned' in maths when basic arithmetic and logic are all that are necessary. People don't have to like something to be able to do it, but it's in their (and everyone's) best interests to think logically and critically, and they should feel confident they can do so in all areas of life instead of believing they're just no good at maths and switching off because they haven't learned or remembered the 'rules of maths'. I only have a GCSE in maths myself, and I'm certainly not academically gifted.

It's the opposite IMO. If people are told they should be able to solve everyday maths problems just applying inate logic, but they can't, that will discourage them. They're told they should be able to do something without being taught how and if they can't they're illogical.

If you show them rules and techniques to solve problems, then they can use them next time. It's no different to teaching children how to add up. Start at the right, add the digits, if it's over 10 carry one etc. Some people may be able to work out how to add or multiply two numbers inately, but most will use techniques and rules they were taught at school.

Same for more advanced stuff, like compound interest, mortgage repayments, algebra etc. They don't need to "remember" rules, they can look them up. But if they use them regularly the main rules will stick.

It's not a case of they 'should' be able to solve everyday maths problems with innate logic; they can do it. It's the inherent 'can-do' attitude, instead of dismissing things outright because they're confronted with lines and lines of letters, numbers and symbols. 'Good at maths' in the vernacular is more akin to Carol Vorderman or Rachel Riley quickly formulating arithmetic solutions to hit seemingly impossible targets (within 30 seconds); that is far more difficult than understanding consumer finance, which is more akin to finding five-letter words.