What is Large numbers: Definition and 37 Discussions
Numbers that are significantly larger than those typically used in everyday life, for instance in simple counting or in monetary transactions, appear frequently in fields such as mathematics, cosmology, cryptography, and statistical mechanics. The term typically refers to large positive integers, or more generally, large positive real numbers, but it may also be used in other contexts. The study of nomenclature and properties of large numbers is sometimes called googology.Sometimes people refer to large numbers as being "astronomically large;" however, it is easy to mathematically define numbers that are much larger even than those used in astronomy.
Kurzesagt in a Nutshell said that the number of possible protein combinations the human body can have is 6.8 x 10^495. I asked GPT to multiple it by 20 million (which is the hypothetical number of possible alien civilizations in the Milky Way galaxy give or take). The chatbot gave me 1.36 x...
Was watching a youtube on Grahams number last night and its discoverer Ronald Graham. He talked about how many algorithms can calculate the ending digits of the number (its a power of 3) but the first digit is unknown. Guessing this is generally true of all incomputably large numbers that are...
Hi everyone.
I haven't been here in years, I'm surprised the account still works.
Anyway. I have a mathematic thought/question that I really want to learn about. I realize this isn't going to be the easiest thing to explain if it is even possible, so please forgive me.
So, What I want to do...
Paul Dirac proposed a hypothesis called "Large Numbers Hypothesis" (https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis), where he basically stated that, if he was correct, laws of physics would change with time.
But what about fundamental laws and constants? (Not only 'effective'...
Prominent physicist Paul Dirac proposed a hypothesis that indicated that constants and laws of physics would evolve with time into different constants and laws of nature (https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis)
This hypothesis was used by Robert Dicke...
Hi,
Mostly i work with Octave / Matlab but i am trying to get into python also.
Lately i have a couple problems where my numbers can't be represented in binary64 or float64 default format because they exceed the max of 1.8x10^308. Is there a common way people deal with this (without toolkits)...
I am using complex numbers and was wondering if there's any way that I can get output to match my exact input when performing basic arithmetic on them. For example, if I use type = complex_ or complex256, with A = 1. and B = 6.626 x 10^(-34), then C = A*B yields C = 6.626 x 10^(-34) as wanted...
Hi,
I'm a little unsure how to input large numbers into the TI-83 calculator using invNorm and normalcdf. Here's the question to the problem:
A study of VCR owners found that their annual household incomes are normally distributed with a mean \$41,182 and a standard deviation of \$19,990...
Hi, I'm trying to figure out how to compute probability related to a problem I am tackling for work, and I think I have a handle on how to do it with smaller numbers, but no idea how to approach it for larger numbers. (And I need to explain the answers to a judge in simple terms). So here is...
Homework Statement
(a) Find the remainder when 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divided by 5.
(b) Generalize this resultHomework Equations
Congruence Modulo
a\equivb mod n
also
a=n*q+b where q is some integer.The Attempt at a Solution
The remainder for 1^99 would be 1.
The remainder for...
Homework Statement
Recall that log 2 = \int_0^1 1/(x+1) dx. Hence, by using a uniform(0,1) generator, apprximate log 2. Obtain an error of estimation in terms of a large sample 95% confidence interval. If you have access to the statistical package R, write an R function for the estimate and the...
I've been picking up a few undergraduate texts to patch up some education gaps that need filling. I'm brushing up on statistical mechanics right now, and I'm utterly bewildered by something Daniel Schroeder does in "Introduction to Thermal Physics" in section 2.4:
OK. Come on, this is...
which is greater as n gets large, f(n) = 2^{2^{2^n}} or g(n) = 100^{100^n}
instinctively I'd go with f(n) but I have no idea of actually showing that f(n) would indeed get larger, obviously sticking in values of n doesn't particularly work. A method I was thinking was to show many digits...
Sorry it's my first time posting so I am not sure if latex works here...
I have been trying to understand the proof of WLLN using Chebychev's inequalities, and here are my problems:
I know for the Strong Law of Large Numbers,
if n→∞, Ʃ(1 to n) σi ^2 / i^2 < ∞ => SLLN is satisfied...
Disclaimer: If this is the wrong place for this, I apologise, this probably comes somewhere between QM, Atomic, Linear algebra and a spoonful of Quantum chemistry for good measure.
Anyway, for a group of non interacting (mean field) electrons, moving in a potential generated by nuclei and...
Homework Statement
I need a thorough proof of the weak law of large numbers and it must use moment generating functions as below.
Homework Equations
The weak law of large numbers states that given X1...Xn independent and identically distributed random variables with mean μ and...
I stumbled upon a math question, at the glance of it, seemed easy.
One is supposed to find the exact value of this square root:
√30*31*32*33+1
They are all under the square root operator and Fundamental BEDMAS/BIDMAS applies of course.
The trick here is when the condition states that one...
Homework Statement
Evaluate (16^1000 - 18^2000)(mod 17)
Homework Equations
I'm not sure how to go about doing this, but I realize it has something to do with the pattern from the last digit obtained from the 2 large numbers
The Attempt at a Solution
I need to factorize large numbers (some of them have about 200 decimal digits). Wolfram alpha is a dead end and programming with python is not working for me too. Any suggestions?
Homework Statement
If \overline{X}_n converges to \mu, does \frac{1}{\overline{X}_n} converge to \frac{1}{\mu}?Homework Equations
http://mathworld.wolfram.com/WeakLawofLargeNumbers.htmlThe Attempt at a Solution
\frac{1}{\overline{X}_n} = \frac{n}{X_1 + \cdots + X_n}...
I was just thinking why is it hard to remember a 15 digit number for example?
(some people might not have trouble, but I think the majority would find 15 digits difficult without seeing it more than once).
But I think it's because we assign an entire word to a number. For instance, remembering...
Does the law of large numbers really apply directly to betting systems? For example, in American roulette the house advantage or "edge" is 5.26%, and smart players know that, as a consequence of the law of large numbers, you will lose 5.26 cents of every dollar bet in the long run. This is...
I am 31 and just started back in Math. My first class is Intermediate Algebra. I am sloving equations that force me to factor large numbers. Not sure if this is a skill that I was supposed to rember from high school, but nevertheless it is taking me a long time to do so. Can anyone tell me what...
What is the rate of convergence of the law of large numbers?
ex.
if
lim_{n \rightarrow \infty} \frac{1}{n} \sum Z_n = \mu
1. can we say that the sum converges to \mu as n^\alpha for some \alpha\in \Re?
2. If so, what is the value of \alpha?
Thanks,
NOTE: This is a long post. If you want, you can skip ahead and start reading where I write "Things get really juicy".
The strong law of large numbers:
http://upload.wikimedia.org/math/1/4/6/14624d8f38c79d9fde049910b62d9d2c.png [Broken]
The stuff in parentheses is an event. But what is...
I have this question which I am puzzled from, hope someone can help me here.
Prove/disprove:
If X[n] is a sequence of independent random variables, s.t for each n E(|X[n]|)<5 (E is the expecatation value) and the stong law doesn't apply to this sequence, then the same law doesn't apply on...
Hi
I was studying the WLLN and the CLT. A form of WLLN states that if X_{n} is a sequence of random variables, it satisfies WLLN if there exist sequences a_{n} and b_{n} such that b_{n} is positive and increasing to infinity such that
\frac{S_{n}-a_{n}}{b_{n}} \rightarrow 0
[convergence in...
I had this dumb though the other day. I can't help wonder if there would ever be a reason to use the convolution theorem to multiply large numbers. It is used to multiply polynomials. But you would need an awful lot of digits to get any efficiency advantages from it and it would not take care of...
In doing a problem, I considered N (a large number, in the range 100,000-1,000,000) raindrops, falling into A (fixed at 100) segments on a roof, distributed using a random number generator I programmed. In considering the number of raindrops that fell into a given segment, the average would be...
For the Strong Law of Large Numbers, as far as I know it applies when, let say, the random variables {Xn: n=1,2,...} are iid, hence uncorrelated, their second moments have a common bound and they have a finite mean mu.
What else I must consider? Is there anyother consideretion or case when the...
Well um, I was wondering...w/o simulation,
How do you prove the Law of Large Numbers?
And what's Chebyshev's Theorem? (somewhere, i heard it was mentioned, but what is it?)