Different Types of Infinity, arithmetic vs geometric vs exponential growth also energy vs power

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Vovk

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Jul 29, 2019
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<rant>
Energy is the amount of work an object can do - period. In minecraft, energy is represented by MJ, EU, Bluelectric Charge and Factorization charge.

Power is the amount of work an object can do over time. In minecraft, power is represented by MJ/t, EU/t, and Watts.

Infinite energy is quite easy to do in minecraft. The oil fabricator loop is a good example. Oil -> Refinery -> 36HP boiler -> Engines -> oil fab -> loop will provide a constant trickle of energy at FINITE POWER.This can also be thought of as arithmetic growth of energy since you follow an arithmetic pattern (10+10+10+10+10+10+etc)

When you want to do automation with constantly running machines, you want to think about power and not energy. If your machines use 60 MJ/t and you produce 20 off yer fancy oil loop, you are still running at well under optimal and you are still limited in time. Infinite energy assures you that your machines will continue to work forever, but it doesn't mean that they will work very quickly.

Infinite power is a bit trickier to do. The best example would probably be a factory powered by hybrid solars which is automated to turn its UUmatter into more hybrid solars which are placed by turtles which expand forever. This infinity is much larger than the previous infinity and will be able to supply infinite power over time. You can think of it as a geometric growth of energy (10*10*10*10*10).

If you constantly make machines that require more power as they progress in time, you will need a factory that builds those solar panel factories and thus make use of an even bigger infinity. You can think of this as exponential growth of energy (10^10^10^10^10)

the point is - just because things create infinite energy doesn't mean that they will suit your needs. Finding an early game finite source of energy with a great power output (like fuel) will probably be more useful to you than an infinite source of energy (like a lava loop) until you get enough resources that your power source doesn't matter any more.

</rant>
 
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Scroff

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Jul 29, 2019
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Pandemoneus said:
Infinity is infinity... there's no "this infinity is bigger than that infinity". :p
Click to expand...

FYI there's a least two different, well defined, infinities. The smaller is the cardinality (i.e. size) of the set of natural numbers (starting at 0, and if n is a natural number then so is n+1). The larger is the "cardinality of the continuum" which is the size of the set of real numbers (include pi, e, 1/7 etc etc). Fun fact: there are more real numbers between 0 and 1 than there are natural numbers.

No physical system has an infinite amount of anything, which I guess is why people use the term renewable.
 
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Whovian

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Scroff said:
FYI there's a least two different, well defined, infinities. The smaller is the cardinality (i.e. size) of the set of natural numbers (starting at 0, and if n is a natural number then so is n+1). The larger is the "cardinality of the continuum" which is the size of the set of real numbers (include pi, e, 1/7 etc etc). Fun fact: there are more real numbers between 0 and 1 than there are natural numbers.
Click to expand...

There are plenty more. :) In fact, the common definitions are basically,

let Aleph_0<Aleph_1<Aleph_2<..., where Aleph_0 is the number of natural numbers. (These are generally called the cardinal numbers.)

(Most think Aleph_1 is the cardinality of the continuum, though no one has proven this yet.)

Anyways, from what I can make of the OP, you're basically saying that one function is "more infinite" than the other if it dominates the other; that is, f(x)/g(x)->0 as x grows large. They have the same "sort" of infinity, infinity basically just means "larger than any real number" in calculus terms, but yes, one function dominating the other can be quite useful when it comes to engineering like this. While you lack rigor in understanding what larger infinities *mean,* you bring up some very good points, and I wouldn't blame you for not quite understanding, it's pretty much impossible to if you haven't studied calculus in formal terms.

(Oh, and geometric growth *is* exponential growth.)
 
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whizzball1

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Jul 29, 2019
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Pandemoneus said:
Infinity is infinity... there's no "this infinity is bigger than that infinity". :p
Click to expand...
NumberPhile made a video on this.
There are many types of infinity, and the two main categories are Countable and Uncountable Infinity.
Countable Infinities are like the list of Whole Numbers, 0, 1, 2, et cetera, et cetera, or the list of Natural Numbers, 1, 2, et cetera, et cetera.
But what about Uncountable infinites?
Consider Rational Numbers (Positive and Negative Integers).
In order to start counting, you would have to go to the very beginning of the number line.
Which of course, is impossible.
Decimal Numbers.
Start from 0.
That's easy.
But then you have to find the next smallest number.
That would have infinite zeros before the one.
So no for Decimals.
Fractions?
Smallest fraction?
Start from 1/Infinity.
Nope, nope, and nope.
But this is much better explained in this video:
Have fun!
 
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whizzball1

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Bellaabzug21 said:
Actually, if the quadrileph of the chromatical hernia is equal to five then the secubilaterus of your boiler's power will lower causing a slip in the quadrilateral strength of your faucet thus causing your power to be equal to a compatoratory nil.
Click to expand...
You are just spouting out terms you don't even know.
Hernia is an injury to internal organs.
Seriously...
Don't try to make yourself seem smarter than you are.
 
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