Ashmnafa
Veteran
Sorry, allow me to correct myself. A horizontal line has a slope of zero.
Why can't people think for themselves?
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Sorry, allow me to correct myself. A horizontal line has a slope of zero.
MichaelP.
Veteran
A slope needs to be a quantifiable number. You should be able to plug it into equations, and because a vertical line's slope is (Y2-Y1)/0 , and you cannot divide by 0, the slope is undefined.
oprah62
Veteran
Ashmnafa
Veteran
That sounds like a better explanation of what I just said. Thank you Mr. Perkins.
BigGreen
Veteran
But what about people who are incapable of thinking for themselves like the mentally challenged
oprah62
Veteran
Posted that before I asked lol.
I had this weird way of remembering it. On flat ground (horizontal) you're happy because you're safe, but if you're falling down (vertical) you're screaming NOOOOOOO.
MichaelP.
Veteran
HOYVUX FTW
cmhardw
Premium Member
I disagree with this. A slope doesn't need to be a quantifiable number. It's just that cool things like Calculus and Modern Science happen when slope is a quantifiable number.
A line could be "really slopey" or "way totally not slopey" also. There is no need for a line to have a numerical slope, but it's arguably much better when it does have a quantifiable number slope.
Chris
MichaelP.
Veteran
In that case we don't need any numbers at all. We can just say "super big" or "eency weency". In my opinion this isn't really relevant to the discussion. I used "needs" because for our purposes, the slope needed to be quantifiable.
Dene
Premium Member
And what were our purposes again?
cmhardw
Premium Member
Ok point taken. I will agree that it is much better to have a quantifiable number for the slope, as this clearly leads to lots of fancy shmancy maths
However, and this hits on Michael point about an undefined slope:
Why is a vertical line slope (Y2-Y1)/0?
In fact, why is slope even defined as \( \frac{y_2-y_1}{x_2-x_1} \) at all?
Hint: I'm not being facetious here, there actually is an answer to this question, and it is very closely related to Michael's point that a vertical line absolutely can have a defined slope.
Chris
Cubenovice
Forever Slow
fixed
cmhardw
Premium Member
I do this all the time. I don't see the problem with it, often office chairs are adjustable so can get higher and especially if you're on carpet it isn't that hard to balance and usually it is the only chair around.
blade740
Mack Daddy
If you must put a numerical value to it, I would say that a vertical line has a slope of infinity. Common sense tells me that zero goes into any number infinity times, and so n/0 should be infinity.
Or, to look at it another way, as a line tilts from 0 degrees (horizontal) to 90 degrees (vertical) the slope approaches infinity.
Or, to look at it another way, as a line tilts from 0 degrees (horizontal) to 90 degrees (vertical) the slope approaches infinity.
cmhardw
Premium Member
*Directed not at anyone in particular, but the thread in general*
The point I am trying to make is the same point as Michael was trying to make in the OP. I'll prove to you what I mean. A vertical line's slope is undefined. Like Michael, I disagree that this must always be the case. A vertical line's slope can be defined. In fact, I can provide a meaningful definition of slope such that it is still a scalar quantity, still lets us evaluate derivates and integrals and all that fancy awesome stuff, and yet a vertical line has slope -1
Can anyone else? More importantly, do you see the point that Michael is trying to make?
Chris
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Hadley4000
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I don't think people are incapable of thinking for themselves, I think they're just too lazy.
It seems that recently (especially because of the internet) that there are more and more people "questioning authority". Unfortunately it is going to extremes and irrational conspiracy theories are spreading like a disease. It is one thing to be skeptical and think for yourself after considering all the evidence, but abandoning rationality and blindly following some conspiracy theory that is labeled as "thinking outside the box" is very different.
It is good to think for yourself, but if you don't have all of the unbiased facts, all you will end up doing is regurgitating crap that other people say.
There are some thing that you learn in school that are either plain wrong or over simplifications. It is good to question authority as long as you have a valid reason to do so. I am pretty sure that there are more free thinkers now than there have ever been.
It is good to think for yourself, but if you don't have all of the unbiased facts, all you will end up doing is regurgitating crap that other people say.
There are some thing that you learn in school that are either plain wrong or over simplifications. It is good to question authority as long as you have a valid reason to do so. I am pretty sure that there are more free thinkers now than there have ever been.
Cubenovice
Forever Slow
Interesting discussion going on here.
Since I'm not that smart or educated in the subject of math I'll try to summarize my learnings of this thread
Horizontal line: slope is zero / something = zero
Vertical line:
The general Idea: slope is something / zero = undefined so we're not even sure if we can use the term "slope" for this situation.
However it seems that scalable quantity actually can a be assigned. (Chris)
Right?
Let's complicate things for myself and compare parallel lines:
To my understanding two straight lines are considered to run parallel when they have identical slope.
Take two horizontal lines, both have an identical slope (zero): they are parallel
Now we take two vertical lines:
General idea: both have an "undefined" slope. So my question is: can we even claim that they are parallel? (Math people?)
Scalable quantity idea: can we use this to show that two vertical lines have identical "scalable quantity" and thus? are parallel?
Since I'm not that smart or educated in the subject of math I'll try to summarize my learnings of this thread
Horizontal line: slope is zero / something = zero
Vertical line:
The general Idea: slope is something / zero = undefined so we're not even sure if we can use the term "slope" for this situation.
However it seems that scalable quantity actually can a be assigned. (Chris)
Right?
Let's complicate things for myself and compare parallel lines:
To my understanding two straight lines are considered to run parallel when they have identical slope.
Take two horizontal lines, both have an identical slope (zero): they are parallel
Now we take two vertical lines:
General idea: both have an "undefined" slope. So my question is: can we even claim that they are parallel? (Math people?)
Scalable quantity idea: can we use this to show that two vertical lines have identical "scalable quantity" and thus? are parallel?
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