Infinity – More about infinity, 1/infinity, Why is it that 1/infinity equals 0?
Infinity is a concept, not a number. We know we can approach infinity if we count higher and higher, but we can never actually reach it.
As such, the expression 1/∞ is undefined. Whatever we can do is look at what value 1/x approaches as x approaches infinity or as x gets larger and larger.
More about Infinity
1. It is the idea of something infinite
- Just think of “infinite” or “unlimited.”
- If there is no reason for something to stop, then it is infinite. Infinity does not grow
2. It does not “grow
- Infinity does not grow. If ∞ + 1 = i∞, then the literal presumption is that it has somehow grown. But, It didn’t.
3. It is not a actual number
- It is an idea—the idea of something endless.
- It can not be measure. Even these distant galaxies cannot compete with infinity.
4. It is simple
- It is easier than things that have an end. Because when something has a lot, we must determine where that end is.
5. The infinity symbol
- The ∞ symbol is eight on its side, often called lemniscate; mathematician John Wallis invented this symbol in 1655.
- It is not a numeral, so you can’t say that 1 divided by infinity equals anything. In practical problems, you may find an approach to infinity.
- Since Lim x→∞1x=0 Lim x→∞1x=0, you can usually get away with using zero when a problem appears to divide 1 by ∞.
- Remember that it’s a limit, not an actual value.
- Most computer double-precision math libraries will give you zero if you divide 1 by ∞.
- In this case, “infinity” is a unique value, which isn’t quite precisely like actual infinity, but it suffices for many practical problems.
- It is the limit of n where n runs to infinity; that’s logical.
- And one divided by ∞ is (the limit of 1 where n runs to ∞) / (the limit of n where n runs to ∞) = the limit of 1/n where n runs to ∞=0
Is 1 infinity equal to 0
- It is not a number; read this over and over until you understand. I’m not trying to sound rude, but it’s a concept we need to know before we move on.
- As it is not a number, and you cannot do simple arithmetic using ∞.
- To illustrate the crazy traffic jams people find themselves in when they say 1∞ = 01∞ = 0, consider replacing the denominator with another number, a real number.
- 12 = 0.512 = 0.5
- I don’t think anyone will find this statement very controversial.
- And we can multiply the quotient by the divisor to get dividends in another true one, without a controversial statement:
- 0.5 x 2 = 10.5 x 2 = 1
- So what if we try to change the assertion that 1∞ = 01∞ = 0?
- We get 0 × ∞ = 10 × ∞ = 1
Infinity multiplied by Zero
- First of all, multiplying zero by any number gives zero, so if we’re going to treat ∞ as a number, then zero multiplied by infinity must not equal 1.
- On the other side, if we were to think of ∞ as a number, I could understand your saying that ∞ multiplied by anything is ∞.
- So if we try to say that zero times infinity equals one, which is a logical sequence of 1∞ = 01∞ = 0, we run into some terrible contradictions.
- You are looking for the limit. Limit allows us to explore what a particular value is aiming for.
- limx → ∞1x = 0 limx → ∞1x = 0
- It means that as x increases, the value 1 / x becomes very small.
- If you could estimate 1 / x for ever-larger values of x, you would get closer and closer to zero until the end of time. But this is not the same as saying that 1∞ = 0.
Why is it that 1/infinity equals 0?
- Let me try to prove it.
- If 1/∞=0, then 1/0=∞.
- Now let, 1/0=x (which we have to evaluate)
- Thus, 1=0*x
- For any value of x (including ∞), 0*x≠1.
- Thus, 1/0 is not ∞, or 1/∞ is not 0.
- 1/∞ is relatively undefined.
- But, the reason you are asking is due to a similar statement that was misinterpreted as 1/∞=0.
- The statement is,
- For, x->∞ 1/x->0. ……(1)
- Remember, the “->” sign means tends to, not equal.
- So, the statement states that if a number gets very close to infinity, then the inverse of the number will get very close to 0.
Is it that 1/∞ equals 0?
- 1/∞ has no meaning, as ∞ isn’t a number, as do you; you can’t do numerical calculations with it.
- Mathematicians get around this using the limit operation and talk about the limit as X tends to infinity some expression.
- In this case, the term would be 1/X. (This is an abuse of language if you want to be pedantic.)
- However, the definition of the limit doesn’t have the word ‘infinity’ in it. The limit is that number that the expression gets close to as X gets very big.
- It’s more potent than that; the term can be made arbitrarily close to the value as long as X is sufficiently large.
- So, as 1/X can be as small as you wish, as long as X is big enough, the limit is zero. Clear? And not infinity insight.
- MORE INFO:- itechits
Superfoods and Nootropics: Supplements that Make the Perfect Combo
Superfoods and nootropics are two of the most popular supplement categories on the market today. And while they both offer…
How Does Vagus Nerve Stimulation Work?
How Does Vagus Nerve Stimulation Work? – Vagus nerve stimulation (VNS) is a treatment used for various conditions like epilepsy…
5 Tips For Properly Walking With Baby In Winter
Tips For Properly Walking With Baby In Winter – While it’s easier to walk during the summer when you can…
What is the Best Way to Get an Instant Personal Loan Online?
“The Core of Beauty is Simplicity” – Paulo Coelho What is the Best Way to Get an Instant Personal Loan…