All numbers are capable of equivalency. So 1 = 1, 2 = 2, etc.
But all physical objects are unique within time and space. So abstracting an object into a number removes that uniqueness.
Unless you count repetition of matter within infinite space. But even if you did, matter is in constant flux. So one object will never be identical to another.
The whole point was that numbers are an abstraction of something real, like a shadow or reflection. An abstraction will never completely encompass the entire nature of a natural object.
but you can’t do that, you can apply the same logic/reasoning to dividing by zero. (You do know why dividing by zero is undefined right) Im sure you don’t know, but if you divide by zero then 1=2=3, etc. You can’t do that because then you have information loss. You cannot have information because loss it impossible. Simple laws of Thermodynamics say so, Conservation of Energy, Newtons Laws of Motion, etc, even in black holes, there is no information loss ever.
If there was then you couldn’t even trust your memories or yourself, how do you know that what you remember is real. How do you know that you where you yesterday? Why would you trust getting in a car if there was information loss?
1 never equals 2
wait, never mind, I though I saw 1=2. fucking retard. BTW, you never did answer the question. It was never relevant because you where the one to bring it up
I think this essay is worth a read. Thoughts of a professional mathematician on math education. He doesn’t stress applications so much as learning math for its beauty and artistic aspects (I don’t see any dichotomy between beauty and application, though- unlike Hardy, whose early 20th century, upper class English attitude towards “ugly” math that’s actually useful is pretty infuriating). He nicely explains the problems with our current system, and is only slightly hyperbolic at times…the math pun is unintentional.
you post are generally more interesting than most
but I am confused as to what you are saying:
i thought at first your point was that Math as it is taught is not practical because of its inability to be applied to real life. Now you are saying that applying to real life is not precise, and practicality is unimportant ( i think practcality is overrated myself).
Are you saying math is imperfect because people cannot make models which perfectly represent reality?
I dont know what that has to do with math but; do you know why they are called models?
and;
Do you know what math is?
…more or less, a language of numbers and logic that is limited only by the one that uses it. If you accept such a definition, how could it be imperfect? Do you accept?
in calc I always thought areas under curves that have limits were funny. Calculating the area under a curve thats limit is zero. It is like the teacher is telling me that I can paint an infinite area with a finite amount of paint.
does such an example support Matriarch’s perspective?
hahaa
ah tired
i think there is a crossed line here, btut I was wrong anyway
I was remmebering incorreclty (confused with Gabriel’s horn?):
predtend I said this thenthis:
‘It is like the teacher is saying that I need an infinite amount of paint to cover a finite area’
I think it only sounds like that if you take the total sum of an infinite amount squares/rectangles which have an infinitely small width at face value.
i should not take at fac value?
i should pretend magic (logic jump)?
is that the argument you are using to invalidating my doodoo thought experiment?
0 = 1?
Is it? IIRC, the area under that curve as it approaches infinity = 1
Well it sounded like you forgot that the area under the curve is an integral. You have an infinite amount of squares between a set interval, but the total sum of those infinitely small rectangular width’s (infinitesimals) have a defined real value.
0=/1
if anything its more like infinite sum = some value
Nope, it diverges. You’re thinking of the limit from 1 to infinity as x approaches infinity of 1/x^2. I need to learn to type integrals on texify. Also, the summation of 1/x = infinity, so that’s an easy way to tell that the integral does as well.
ah, damn. You are right. But looking at the graphs, my mind is full of fuck.
Damn convergence divergence rules. Guess I have to go back and reteach myself that along with taylor series. That particular subject was the hardest (conceptually) in the whole Calculus sequence.
you know that line that the teacher draws on the board to represent the curve approaching the limit of zero under which the area (which is finite) that you are calulating?
well that line goes on forever
In class I used to think sih like: "You can use all the chalk in the world, and still not finsih this line; but the volume underneath is finite? If I had a material that was supersmall in particle size, I would need an infinite amount of this material to cover this finite area"
how dat?
edit:
I always thought of this as a paradox (which is not a failure of math at all), which was my point. but I guess that supersmall material would have to be infinitesimally small in order to work in my thought experiment, which would kindof disssolve the paradox.
i guess im dumb (epiphany), carry on
bedtime
By definition a line is infinite, but the sum of the area under the curve is limited to what ever intervals you need. Until you get to convergence and divergence, shit like
1/x or 1/x^2
yeah, that crap is weird.
The whole concept makes more sense when its applied in E&M Physics. The best example I could think of right now is
when you bring a particle from an infinitely distant point into the system of point charges
IKR. I don’t understand it conceptually either. Also, can you see the image I’m embedding? I typed it on Wolfram and I wanna see if it’ll stay up. If only simple queries like “integral 1/x^2 from 1 to inf = 1” worked on Texify.
If you had an infinite object that decreased at the same rate or faster rate as 1/x^2 yes you could. Problem is there is no such object that we know of. However the math is still valid, it says you could make a tube as long as you want, but the volume can never exceed that number.
The main idea behind infinity is not that it is a hard object rather it means that we can choose how large the number gets.
I mean if you want to see a practical example of a limit is like this. So for this example let me use this limit
As x-> Infinity, lim x/(x+1) = 1
Ok so most people might look at this and say “duh!” or something along those lines, but this statement actually means a lot more than people might realize. In math terms this says “When x is really large, x is approximately x+1”, but let me put it another way. If you have a hundred billion dollars and I give a penny you technically have one hundred billion dollars and one cent. Yet if I asked you how much you have you might say “I have about a hundred billion dollars”. Why? Because in the grand scheme of things the penny is worthless compared to the amount of money you had before. I hardly increased your wealth at all. Yet if you have one penny and I give you a second penny I just doubled your networth.
In fact that limit you see is the mathematical justification for rounding! It basically says we can neglect a small insignificant penny because it is “close enough” to 100 billion as far as we are concerned. In fact most approximations used in science are based off a limit of some kind.
PS Just so no one in the thread is confused. I define a penny as a small round partially copper object equivalent to 1 US cent as defined by the Department of the Treasury of the United States of America which was first founded in the late 1700s-early 1800s. This round object has an average weight of 2.81 grams if made after 1982 and an average radius of 19mm. It is not perfectly circular, but is approximately circular. The atoms of the penny are in a face center cubic structures who’s ensemble average deviates from the ideal solid. The copper atoms have a Jan Teller Distortion about their x^2-y^2 axis, they are inactive under NMR and highly active under X-Ray diffraction. These pennies react with Nitric acid to form copper compounds along with other base metals dissolved in it. They typically are found in ash trays, hobo’s pockets, cash registers, and other places in the US. They are useful for throwing at your sister or that annoying dog that pees in your yard.