Ustulo
Well-Known Member
Ти си кебаб. Морам те уклонити.דצכ
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Ти си кебаб. Морам те уклонити.דצכ
לגלגל
דלכללהדגלגל גלגל כלכלה לפשלה
Calculus was a fun class for me especially since the analytic geometry part helped visualize fitting slopes to lines and adjoining numerous boxes under curves.
Can I have in phonetic spelling? Because that makes no sense.Ти си кебаб. Морам те уклонити.
QUESTION: Which line has more points?
QUESTION: Which rectangle would have the greater height?
I guess the first question should have read "which line has more possible points?" and should not have had the existing endpoints marked.They both have either 2 points or infinite points depending on which type of geometry you want to apply.
You can say that both line segments contain an infinite number of points but each of them only HAS two points.
They height of both will approach infinity but not reach it, as the requirement of a rectangle and the concept of area fail as the edges come together and the rectangle becomes a line segment.
Wait. Does this mean that a line doesn't have a width of zero? Do they join when the distance between them is something other than zero?
We aren't, however, attempting to list the possible points, just determining which has the greater infinity. I believe my argument still stands - that the line with a greater length has a greater amount of points (or a lesser distance to the next point if the distance is greater than the length of the line). My reasoning here is that the basics of math still apply: no matter the distance between points, the line with the greater length will have more points. Extrapolating that to an infinitely small distance between points, the line with the longer length would continue to have a greater amount of points, even though they both have an infinite number of points.
I am having trouble seeing one as taller than the other. To me, this is like comparing two dead bodies; one may have died first, but the other is right there with it now. Like you said, the 5-area may approach its limit more quickly, but the 4-area is approaching the exact same thing. I have heard bits and pieces about other types of limitless-ness (and love the Numberphile video on it. /me 's Numberphile.) but I don't see the difference here. When comparing solely where two things are, "I got here first" doesn't seem relevant.By definition of a mathematical limit (which the two of us have discussed before), it is the value that our function of interest converges on as the domain becomes sufficiently close to, though not necessarily reaching, the location of interest.
In this case, I observe the height of the two rectangles as a function of its width. As the width of both rectangles becomes smaller and smaller, the 5-area rectangle's height approaches infinity faster than the 4-area rectangle. Hence, I arrive at the conclusion I draw in my previous post. Granted, the limit of the heights two rectangles are both infinity as their widths go to zero. Infinity is not a real number, so, as Gurw said, I can only draw a qualitative answer for this.
The point being, neither can truly reach infinity - since to remain a rectangle, the lines can never truly merge. They may be extremely tall - but the closer the lines get, the greater the difference between the heights of the two rectangles.I am having trouble seeing one as taller than the other. To me, this is like comparing two dead bodies; one may have died first, but the other is right there with it now. Like you said, the 5-area may approach its limit more quickly, but the 4-area is approaching the exact same thing. I have heard bits and pieces about other types of limitless-ness (and love the Numberphile video on it. /me 's Numberphile.) but I don't see the difference here. When comparing solely where two things are, "I got here first" doesn't seem relevant.
But their limit is infinity. Whatever height rectangle 5 reaches, the other can reach with a shorter width.The point being, neither can truly reach infinity - since to remain a rectangle, the lines can never truly merge. They may be extremely tall - but the closer the lines get, the greater the difference between the heights of the two rectangles.
Their limit is actually 1 unit (whatever unit we're using, however small) less than infinity. If the limit were actually infinity, the lines could merge. However, they can't. So the rectangle with the area of 5 will have a much greater height, and will only widen the gap that much more as you approach 0 width.But their limit is infinity. Whatever height rectangle 5 reaches, the other can reach with a shorter width.
EDIT: Another way of looking at it is that they ALWAYS have the same height, and rectangle 4 simply gets "skinnier" more quickly.
Not quite, but close enough. It's Serbian.Too soo kebab. Morawm meh ooklonuhmuh.
If memory serves, anyway. It's been a couple years since I've had to read ukranian text. Though I'm guessing that's probably a russian dialect, because I don't recognize some of the words.
*with the exception of infinity itself - since that would mean the rectangles had become single lines -Therefore, no matter what number you choose through infinity,
I never said infinity has a limit. I said it exists as the goal which can never be achieved.Infinity has no limit, infinity is not a number. The concept of infinity is that it never ends, and if it never ends you can never perform ordinary mathematical operations on it.
The widths of both rectangles get endlessly closer to - but never actually reach - zero, so both rectangles have an immeasurable height, hence why we term that they are infinitely long. If we were to take the problem into a real world universe rather than the fictitious one where points and lines consume no measurable space, we would be able to describe the problem with real numbers and find that the rectangle with the larger surface area would finish with a greater height when the walls of the rectangles rub up against one another.
*with the exception of infinity itself - since that would mean the rectangles had become single lines -