# Do parellel lines ever meet?

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Here's another one of those problems you encounter when things converge to 0.

By definition, parellel lines are always the same distance apart, but my maths teacher argues that what happens an infinite distance across the lines is mathematically vague.

Say you consider the gradient of two lines to the horizontal. If their gradient is 1 they'll meet after a short distance:

\

/

As this gradient becomes smaller, the lines meet after a further distance. Hence as the gradient tends towards 0, then the lines meet at an infinite distance.

Is there a flaw in this logic?

By definition, parellel lines are always the same distance apart, but my maths teacher argues that what happens an infinite distance across the lines is mathematically vague.

Say you consider the gradient of two lines to the horizontal. If their gradient is 1 they'll meet after a short distance:

\

/

As this gradient becomes smaller, the lines meet after a further distance. Hence as the gradient tends towards 0, then the lines meet at an infinite distance.

Is there a flaw in this logic?

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#2

(Original post by

Here's another one of those problems you encounter when things converge to 0.

By definition, parellel lines are always the same distance apart, but my maths teacher argues that what happens an infinite distance across the lines is mathematically vague.

Say you consider the gradient of two lines to the horizontal. If their gradient is 1 they'll meet after a short distance:

\

/

As this gradient becomes smaller, the lines meet after a further distance. Hence as the gradient tends towards 0, then the lines meet at an infinite distance.

Is there a flaw in this logic?

**Jamie Frost**)Here's another one of those problems you encounter when things converge to 0.

By definition, parellel lines are always the same distance apart, but my maths teacher argues that what happens an infinite distance across the lines is mathematically vague.

Say you consider the gradient of two lines to the horizontal. If their gradient is 1 they'll meet after a short distance:

\

/

As this gradient becomes smaller, the lines meet after a further distance. Hence as the gradient tends towards 0, then the lines meet at an infinite distance.

Is there a flaw in this logic?

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#3

parallel lines meet at infinity. since infinty is "never", no, parallel lines do not ever meet, unless they are the same colinear.

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#8

(Original post by

All these concepts are meaningless in the 'real world' though

**imasillynarb**)All these concepts are meaningless in the 'real world' though

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#9

(Original post by

In Further Maths we started doing complex numbers, and i find it weird how they use "imaginary parts" in real-life situations. We haven't done much on it though.

**Invisible**)In Further Maths we started doing complex numbers, and i find it weird how they use "imaginary parts" in real-life situations. We haven't done much on it though.

I just remember my chemistry teacher(possibly the smartest person Ive ever known) constantly ranting about how Physicists and Mathematicians come up with loads of *******s to explain things, and how most of it is totally meaningless and irrelevant.

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#10

(Original post by

Dont know anything about complex numbers Im afraid.

I just remember my chemistry teacher(possibly the smartest person Ive ever known) constantly ranting about how Physicists and Mathematicians come up with loads of *******s to explain things, and how most of it is totally meaningless and irrelevant.

**imasillynarb**)Dont know anything about complex numbers Im afraid.

I just remember my chemistry teacher(possibly the smartest person Ive ever known) constantly ranting about how Physicists and Mathematicians come up with loads of *******s to explain things, and how most of it is totally meaningless and irrelevant.

However, what they do is use: i = sq.root (-1)

And you can have imaginary solutions to the equation, in effect. However, they use this concept in real-life situations. As I said, we haven't done much, but it's weird.

For example, you even have graphs called Argand Diagrams, and you can sketch graphs of complex numbers. These are of the form a + bi. There's a real axis and an imaginary axis.

LOL, I'll shut up..

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#11

(Original post by

Well basically, you know when you're trying to solve quadratic equations, when you have a -ve discriminant then there are no REAL Solutions to that equation.

However, what they do is use: i = sq.root (-1)

And you can have imaginary solutions to the equation, in effect. However, they use this concept in real-life situations. As I said, we haven't done much, but it's weird.

For example, you even have graphs called Argand Diagrams, and you can sketch complex numbers. These are of the form a + bi. There's a real axis and an imaginary axis.

LOL, I'll shut up..

**Invisible**)Well basically, you know when you're trying to solve quadratic equations, when you have a -ve discriminant then there are no REAL Solutions to that equation.

However, what they do is use: i = sq.root (-1)

And you can have imaginary solutions to the equation, in effect. However, they use this concept in real-life situations. As I said, we haven't done much, but it's weird.

For example, you even have graphs called Argand Diagrams, and you can sketch complex numbers. These are of the form a + bi. There's a real axis and an imaginary axis.

LOL, I'll shut up..

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#12

**Invisible**)

In Further Maths we started doing complex numbers, and i find it weird how they use "imaginary parts" in real-life situations. We haven't done much on it though.

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#13

Yeah, complex numbers are essentially vectors (a real part and an imaginary part), so they can be used to represent quantities that real numbers can't. They're also useful in solving trig problems, because of a handy identity: [cos(x) + isin(x)]^n = cos(nx) + isin(nx), for all rational n.

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#14

**Jamie Frost**)

Here's another one of those problems you encounter when things converge to 0.

By definition, parellel lines are always the same distance apart, but my maths teacher argues that what happens an infinite distance across the lines is mathematically vague.

Say you consider the gradient of two lines to the horizontal. If their gradient is 1 they'll meet after a short distance:

\

/

As this gradient becomes smaller, the lines meet after a further distance. Hence as the gradient tends towards 0, then the lines meet at an infinite distance.

Is there a flaw in this logic?

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#15

(Original post by

Complex numbers..... asked my teacher to give an example whyd we would need em...he left the classroom

**jaffakidds**)Complex numbers..... asked my teacher to give an example whyd we would need em...he left the classroom

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#16

**imasillynarb**)

Dont know anything about complex numbers Im afraid.

I just remember my chemistry teacher(possibly the smartest person Ive ever known) constantly ranting about how Physicists and Mathematicians come up with loads of *******s to explain things, and how most of it is totally meaningless and irrelevant.

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#17

(Original post by

Probably because he didn't understand any of it.

**Pzyko**)Probably because he didn't understand any of it.

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#18

(Original post by

Not really,something is only deemed correct until it is disproven by someone else. There are probably theories etc. we see as correct which have flaws in them. Even 4ed made a thread that contradicted the theories about duality.

**Invisible**)Not really,something is only deemed correct until it is disproven by someone else. There are probably theories etc. we see as correct which have flaws in them. Even 4ed made a thread that contradicted the theories about duality.

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#19

(Original post by

Or he didn't understand any of it.

**Pzyko**)Or he didn't understand any of it.

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#20

(Original post by

That's irrelevant, he still isn't wrong in his opinion that it's a load of *******s. Even the axiom "angles in a triangle add up to 180 degrees" isn't technically correct. A triangle on a sphere doesn't have angles adding up to 180 degrees, I can assure you.

**Invisible**)That's irrelevant, he still isn't wrong in his opinion that it's a load of *******s. Even the axiom "angles in a triangle add up to 180 degrees" isn't technically correct. A triangle on a sphere doesn't have angles adding up to 180 degrees, I can assure you.

So I repeat: he probably didn't understand any of it.

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