Why does infinity divided by infinity equal one?
How do we know the eternal progression of one infinity doesn't increase at a different rate from the other? In short, I'd argue infinity divided by infinity equals infinity, or perhaps zero.
You're question raises an interesting point. The idea is that infinity isn't actually a number, it's merely a concept. You cannot prove infinity exists without finite proof of it's definition, and you cannot find finite proof of infinity (infinite).
As infinity does not describe a single number and is always augmenting, it is impossible to claim any viable equation basing itself in the finite definition.
This is merely my analysis of the question by the definition of infinity. However, check out http://www.philforhumanity.com/Infinity … inity.html to see the mathematical derivation. According to his logic, which may or may not be flawed (i don't claim to be a mathematician), infinity divided by infinity could equal any positive number, infinity even.
Hope this helps your contemplation.
Some infinities could be larger than others? :-) Indeterminate.
Who says that?
Any number divided by zero equal infinity, right?
x/0 = infinity
x = infinity x 0
x/infinity = 0
if x = infinity
then, infinity/infinity = 0
I am glad you asked and yes infinity over infinity is not always one............At least as we approach infinity. This is the start of the wonderful world of calculus.
Lets look at a couple of examples:
So you are correct in that one side can approach infinity faster than the other. We call these limits which is nothing more than saying we are getting incrementally close to infinity, zero, or another defined number.
Lets first look at something obvious:
x^2/x------------->infinity/infinity=1 as x approaches infinity right?
No, it approaches infinity.
Conversely x/x^2 approaches zero as x approaches infinity instead of 1.
Now, I know you probably saying hey wait a minute x^2/x=x and x/x^2=1/x. So one is infinity and the other is 1/infinity. Actually the way it is written both would be infinity/infinity but you defined something very important and that is a rate at which the numerator and the denominator approaches infinity. That is the fundamental principle here.
This actually will get quite a bit more advanced and there are many more principles to learn. This is approaching the definition of the fundamental principle of calculus. So to be concise your thesis is that one side will approach infinity faster and that is correct.
I hope this helps.
Anything divided by itself is equal to unity.
X/X = 1, by definition. When we substitute infinity for X, the answer is still 1.
by ngureco 10 years ago
Any Positive Number Divided By Zero Is Positive Infinity. What Is Zero Divided By Zero?And Any Negative Number Divided By Zero Is Negative Infinity.
by JITENDRA 9 years ago
What is the value of zeroth power of any number?This question is related about the magic value of power of any number
by ngureco 13 years ago
Any umber Divided by Zero is Infinity. How do I Overcome this Bug of MS Excel giving me #DIV/0! ?Of course #DIV/0! is not infinity.
by PhoenixV 6 years ago
Does The Quotient Of 22 Divided By 7 Exist?
by Disillusioned 8 years ago
I took my 30-days page views count; divided it by 30 and further divided it by the number of published hubs. Thus I got a fair representation of my average number of visitors per day per hub. It comes to a whopping 1.6! How about yours?
by Grace Marguerite Williams 6 years ago
What number can be divided by 7, 9, & 11?
Copyright © 2023 The Arena Media Brands, LLC and respective content providers on this website. HubPages® is a registered trademark of The Arena Platform, Inc. Other product and company names shown may be trademarks of their respective owners. The Arena Media Brands, LLC and respective content providers to this website may receive compensation for some links to products and services on this website.
|HubPages Device ID||This is used to identify particular browsers or devices when the access the service, and is used for security reasons.|
|Login||This is necessary to sign in to the HubPages Service.|
|HubPages Traffic Pixel||This is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.|
|Remarketing Pixels||We may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.|
|Conversion Tracking Pixels||We may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.|