And does centrifugal force have an effect on gravity? Q: What would happen if an unstoppable force met with an unmovable, impenetrable object? Q: Why do heavy objects bend space and what is it they are bending? Does it mean that we’re missing something? We can add an odd number but it comes from a different set. Same for an infinitesimal. Can “wave function collapse” be used to send information? Again, there is no real reason to actually do this, it is simply something that can be done if we should choose to do so. What is the process of developing a picture of a higher dimensional object? Q: How many people riding bicycle generators would be needed, in an 8-hour working day, to equal or surpass the energy generated by an average nuclear power plant? Depending upon the context there might still have some ambiguity about just what the answer would be in this case, but that is a whole different topic. The direct use of the infinity symbol in mathematics arises in order to compare the sizes of the sets such as the set of counting numbers, the set of points in the real number and so on. Q: How is the “Weak nuclear force” a force? Q: Why is Schrodinger’s cat both dead and alive? An even number can be written as (even #)/2 results in a modulo of zero. Q: Can free will exist in our deterministic universe? Infinity is a limitless quantity that is greater than every real number. Q: Why does saliva boil in the vacuum of space? Q: What causes friction? Q: How can the universe expand faster than the speed of light? Let’s transform the question: is “sqrt(2) * X” rational or irrational for large X? To see a proof of this see the pdf given above. What are we even looking at? How do we know that someone alive today will someday be a common ancestor to everyone? How can one infinity be bigger than another? We could also do something similar for quotients of infinities. Q: Can one truly create something from nothing? Q: What is infinity? If I’m riding a beam of light and I throw a ball, why doesn’t the ball go faster than light? With infinity you have the following. Q: Why does wind make you colder, but re-entry makes you hotter? What is its relevance? Would any change take place? What’s uncertain in the uncertainty principle? Q: If accelerating charges radiate, and everything is full of charges, then why don’t I radiate every time I move? Pick any number, x, and you find that +  >  + x/2 > x/2 + x/2 = x. Q: How does “1+2+3+4+5+… = -1/12” make any sense? For example, a calculator will show that 2/3 equals 0.6666, but the row of sixes in the number 0.6666 doesn’t end after four digits. Why do phonons and photons have such similar names? Q: How does a scientist turn ideas into math? Q: What are the equations of electromagnetism? I’m just trying to give you a little insight into the problems with infinity and how some infinities can be thought of as larger than others. If so, how small could it be made? Q: What are chaos and chaos theory? INFINITY is not a real finite number either, so the concept of evenness or oddness regarding infinity is not logical in arithmetic. Q: How far away is the edge of the universe? With addition, multiplication and the first sets of division we worked this wasn’t an issue. Q: If atoms are mostly made up of empty space, why do things feel solid? Any number divided by infinity is equal to zero. What is the explanation for this? Q: Are some number patterns more or less likely? For the first time ever, you can buy a book! What’s outside the universe? Q: If you are talking to a distant alien, how would you tell them which way is left and which way is right? Q: “i” had to be made up to solve the square root of negative one. Q: Why do we (people) wave our arms when we fall? well i have always thought infinity to be zero. Q: Why does the entropy of the universe always increase, and what is the heat death of the universe? Physicist: Several questions about doing basic math with infinity have been emailed over the years, so here’s a bunch of them! Q: If gravity suddenly increased would airplanes fall out of the sky, or would it compress the air in such a way that airplanes could keep flying? Q: What is The Golden Ratio? Q: Can planes (sheets) be tied in knots in higher dimensions the way lines (strings) can be tied in knots in 3 dimensions? If the Earth was flat and had infinite area, would that change the answer? Because we could list all these integers between two randomly chosen integers we say that the integers are countably infinite. Q: How many samples do you need to take to know how big a set is? Q: Why does relativistic length contraction (Lorentz contraction) happen? And, no one decides what can we do and not do. You ask whether sqrt(2) * infinity is rational or irrational. Q: What are fractional dimensions? Q: Could a simple cup of coffee be heated by a hand held device designed to not only mix but heat the water through friction, and is that more efficient than heating on a stove and then mixing? Q: What’s the relationship between entropy in the information-theory sense and the thermodynamics sense? Q: What makes natural logarithms natural? Q: According to relativity, two moving observers always see the other moving through time slower. Q: How do you define the derivatives of the Heaviside, Sign, Absolute Value, and Delta functions? Q: Are the brain and consciousness quantum mechanical in nature? Or at least tries to. Q: How do “Numerology Math Tricks” work? Q: What is radioactivity and why is it sometimes dangerous? So, that’s it and hopefully you’ve learned something from this discussion. If we have a set including all of the even numbers it is simply impossible to add another even number. Likewise, a really, really large number divided by a really, really large number can also be anything (\( \pm \infty \) – this depends on sign issues, 0, or a non-zero constant). ∞+i∞? again. However, with the subtraction and division cases listed above, it does matter as we will see. However, despite that we’ll think of infinity in this section as a really, really, really large number that is so large there isn’t another number larger than it. Q: Why isn’t the shortest day of the year also the day with the earliest sunset? Q: Why does going fast or being lower make time slow down? Q: Is it possible to eat all of the ice cream in a bowl? Q: Which is a better approach to quantum mechanics: Copenhagen or Many Worlds? What you know about products of positive and negative numbers is still true here. Q: If there are 10 dimensions, then why don’t we notice them? Why is it better for a rocket to fire at the lowest point in its orbit? (More can be added later). Q: If all matter originated from a single point, does that mean all matter is entangled? Q: What would you experience if you were going the speed of light? Q: Does opening a refrigerator cool down the room? However, when they have dealt with it, it was just a symbol used to represent a really, really large positive or really, really large negative number and that was the extent of it. On a case-by-case basis you can sometimes have “disagreeing infinities” and figure out what they equal. Relativity and Quantum Mechanics: the elevator pitch. Q: In the NEC “faster than light” experiment, did they really make something go faster than light? Q: What is a “measurement” in quantum mechanics? In other words, some infinities are larger than other infinities. Again! Q: What is going on in a nuclear reactor, and what happens during a meltdown? Q: Why does carbon dating detect when things were alive? The symbol for infinity '∞' is called the lemniscate. So, for our example we would have the number, In this new decimal replace all the 3’s with a 1 and replace every other numbers with a 3. Q: What would happen if there was a giant straw connecting the Earth’s atmosphere right above the ground to space? Q: How does instantaneous communication violate causality? But in general, the operations we freely use with ordinary numbers (addition, subtraction, ) need to be considered very, very carefully before they’re applied to infinities (or even zeros). However, INFINITY/INFINITY is an indeterminate expression and can thus be equal to any value, so you cannot make a conclusion. Q: If quantum mechanics says everything is random, then how can it also be the most accurate theory ever? Q: How do lenses that concentrate light not violate the second law of thermodynamics? Is this not a paradox? Most students have run across infinity at some point in time prior to a calculus class. Why? Likewise, this new number will not get the same number as the second in our list, \({x_2}\), because the second digit of each is guaranteed to not be the same. Q: How accurately do we need to know π? Q: Why doesn’t life and evolution violate the second law of thermodynamics? Q: What are singularities? In the case of our example this would yield the new number. Q: Why do we only see one rainbow at a time? Q: What does it mean for light to be stopped or stored? Q: How fast are we moving through space? @The Cool Dude: The way to answer your questions is to replace the infinity symbol with X and ask, does the answer converge as X grows? I know this is a mathematical question, but it does seem a bit over the top. Notice that we didn’t put down a difference of two infinities of the same type. Let’s start by looking at how many integers there are. However, this is clearly not the case. And how did they measure it? Q: What’s up with that “bowling ball creates a dip in a sheet” analogy of spacetime? Q: Does quantum mechanics really say that there’s some probability that objects will suddenly start moving or that things can suddenly “shift” to the other side of the universe? Q: Why is it that (if you exclude 2 & 3) the difference between the squares of any two prime numbers is divisible by 12? What about after the black hole evaporates? Q: If you’ve got different amounts of debt in different accounts with different interest rates, how should you pay them down? Q: According to the Many Worlds Interpretation, every event creates new universes. Q: Is 0.9999… repeating really equal to 1? The infinity symbol ∞ is sometimes called the lemniscate and is a mathematical symbol representing the concept of infinity. The sixes in the number 0.6666 continue as far as a calculator screen will allow; in theory, the number 0.6666 extends forever -- infinitely. Is there a reason to know it out to billions of digits? What is it used for? Q: Who would win in a fight: Gödel or Feynman? Q: What are Feynman diagrams, how are they used (theoretically & practically), and are there alternative/competing diagrams to Feynman’s? You appear to be on a device with a "narrow" screen width (, Derivatives of Exponential and Logarithm Functions, L'Hospital's Rule and Indeterminate Forms, Substitution Rule for Indefinite Integrals, Volumes of Solids of Revolution / Method of Rings, Volumes of Solids of Revolution/Method of Cylinders, Parametric Equations and Polar Coordinates, Gradient Vector, Tangent Planes and Normal Lines, Triple Integrals in Cylindrical Coordinates, Triple Integrals in Spherical Coordinates, Linear Homogeneous Differential Equations, Periodic Functions & Orthogonal Functions, Heat Equation with Non-Zero Temperature Boundaries, Absolute Value Equations and Inequalities. What’s the deal with this orders of operation business? Notice that this number is in the interval \( \left(0,1\right) \) and also notice that given how we choose the digits of the number this number will not be equal to the first number in our list, \({x_1}\), because the first digit of each is guaranteed to not be the same.

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