Queenkit1st
Active Member
My brief, thorough and rambunctuous attempt at debunking myths about the most allusive number in the number line, of the number line or off the number line.
“Infinity is a concept not a number”
“Infinity is always growing”
“Infinity is a number so big we don’t need to think of size anymore”
“You can’t count to infinity”
“Nothing is bigger than infinity”
If you believe any of these statements, read on. (Except the last one because I’m not explaining that today)
Counting to infinity is impossible until you begin to count like a mathematician. What are you doing when you count? You’re assigning each item a number — usually a natural number (0, 1, 2, 3... Integers are negative numbers too also know mathematically as the streak root and their additive inverse). If counting is just a simple assignation to a set of numbers, counting can go instantly from methodically and serially to instantaneous as all one is doing is matching sets up theoretically and not literally (which is what counting is). With this in mind, we can count to any number instantly by matching it up with every number is the base set of numbers (ξ). Doing this with infinity is no harder: you can match up infinite ping pong balls with every natural number. That’s why you often hear about countable infinities.
Because if this we can deduce one thing: since we match it to every finite number, it can’t be a growing set. If we looked at an infinite series in a finite form, we wouldn’t see any change in magnitude. This also leads us to the fact that since it’s not growing and it can be matched like any other number, it bears the fundamental characteristic of a number: to describe the size of a set. (A set is a posh name for what makes up the size of a number. 8 is a set of 8 1s and 4 2s). And finally, the most common mistake of them all: thinking that infinity is in umbrella term for anything that’s so big that if it got any bigger it would be undetectable. This is the hardest to debunk mathematically as logic seems to always say otherwise, but if infinity is really matched with every number in the natural set, there is no way that any finite number could be infinity.
For any mathematical minds out there who are wondering about uncountable infinities or infinity manipulation, I am hoping to post another thing like this as soon as possible.
“Infinity is a concept not a number”
“Infinity is always growing”
“Infinity is a number so big we don’t need to think of size anymore”
“You can’t count to infinity”
“Nothing is bigger than infinity”
If you believe any of these statements, read on. (Except the last one because I’m not explaining that today)
Counting to infinity is impossible until you begin to count like a mathematician. What are you doing when you count? You’re assigning each item a number — usually a natural number (0, 1, 2, 3... Integers are negative numbers too also know mathematically as the streak root and their additive inverse). If counting is just a simple assignation to a set of numbers, counting can go instantly from methodically and serially to instantaneous as all one is doing is matching sets up theoretically and not literally (which is what counting is). With this in mind, we can count to any number instantly by matching it up with every number is the base set of numbers (ξ). Doing this with infinity is no harder: you can match up infinite ping pong balls with every natural number. That’s why you often hear about countable infinities.
Because if this we can deduce one thing: since we match it to every finite number, it can’t be a growing set. If we looked at an infinite series in a finite form, we wouldn’t see any change in magnitude. This also leads us to the fact that since it’s not growing and it can be matched like any other number, it bears the fundamental characteristic of a number: to describe the size of a set. (A set is a posh name for what makes up the size of a number. 8 is a set of 8 1s and 4 2s). And finally, the most common mistake of them all: thinking that infinity is in umbrella term for anything that’s so big that if it got any bigger it would be undetectable. This is the hardest to debunk mathematically as logic seems to always say otherwise, but if infinity is really matched with every number in the natural set, there is no way that any finite number could be infinity.
For any mathematical minds out there who are wondering about uncountable infinities or infinity manipulation, I am hoping to post another thing like this as soon as possible.
but it is then uncountably infinite. 
but it has twisted my brain into a Gordian knot. x
