Infinity and 0 (null set) do not exist

[MDH72]

The statement, "An infinite perimeter can be contained in a finite circle," I believe to be true. I can grasp the concept presented. What I can not, or maybe refuse, to conceptualize is an infinite perimeter. If a path of fractaling is used as a method of increasing perimeter length, eventually the length of an individual new section of the perimeter will have been reduced to the width, or diameter, of a hydrogen atom. Soon, a new perimeter leg will be no longer than an electron.

That is all fine and good. Quantum mechanics can deal with that, so I am told. But I have to reason that there will be a fundamental particle of which nothing else is smaller. When that dimension is reached, perimeter expansion is halted at a finite value. It seems sacrilege to suggest that notion to those that need infinite or infinitesimal values to complete a working equation.

For whatever reason, let's say that the gravitational force of a single grain of sand is in an equation. If the value is considered infinitesimal, and assigned zero, the equation or formula dies there and is useless. The reciprocal is true in that any equation that contains infinity is invalid. That is my opinion anyway and maybe those undefined values are compensated for and this theory is ancient. Just curious.

 

[DaveC426913]

the length of an individual new section of the perimeter will have been reduced to the width, or diameter, of a hydrogen atom. Soon, a new perimeter leg will be no longer than an electron.

You are conflating mathematics and physics.

Pure mathematics is not dependent on the size of atoms. That circle you speak of does not have to exist in the real world. It has no size.

For whatever reason, let's say that the gravitational force of a single grain of sand is in an equation. If the value is considered infinitesimal, and assigned zero,

If you think the gravitational influence of an entire grain of sand (about 10¹⁹ (10 billion billion) atoms is considered zero, you're gonna be real surprised when you hear about the gravitational influence of a single atom of silicon, or an electron.

That is my opinion anyway

Probably best to read up on these matters first and form opinions later.

Just curious.

Curiosity is a good thing.

 

[FactChecker]

Probably best to read up on these matters first and form opinions later.

IMO, that's the quote of the day. I'll have to remember that.

 

[Mark44]

If a path of fractaling is used as a method of increasing perimeter length, eventually the length of an individual new section of the perimeter will have been reduced to the width, or diameter, of a hydrogen atom. Soon, a new perimeter leg will be no longer than an electron.

You are conflating mathematics and physics.

Indeed. Physics is constrained to entities that can actually exist. Objects in mathematics do not have these limitations. A line can have a thickness of zero, unlike any such figure you draw with even the finest pen or pencil.

If the value is considered infinitesimal, and assigned zero, the equation or formula dies there and is useless. The reciprocal is true in that any equation that contains infinity is invalid.

It is already true in mathematics that the infinity symbol is not allowed to appear in any mathematical expression or equation. If we say that some expression has an infinite value, we are really saying that it can be made arbitrarily large in the limit.

BTW, I take issue with the thread title -- "Infinity and 0 (null set) do not exist"
While it is true that infinity does not exist, zero certainly does, as it accurately describes the number of pink flamingoes in my front yard. Also, zero and the null set are not the same things.

 

[FactChecker]

We need to distinguish between the existence of a physical object versus the existence of a concept.
By its own definition(?), the null set does not "exist" as a physical object. But it certainly does as a concept. The set of all humans over 200 feet tall is a null set.

 

[bob012345]

We need to distinguish between the existence of a physical object versus the existence of a concept.
By its own definition(?), the null set does not "exist" as a physical object. But it certainly does as a concept. The set of all humans over 200 feet tall is a null set.

That is until someone falls into a black hole and gets spaghettified.

 

[jedishrfu]

There is one place where infinity is allowed in math as the symbolic end of a limit expression to mean there is no end and it's found in integral limits.

 

[PeroK]

There is one place where infinity is allowed in math as the symbolic end of a limit expression to mean there is no end and it's found in integral limits.

There are several uses of term "infinite", "infinity", or the symbol $\infty$ in mathematics. The natural numbers, for example, is an infinite set. In this case, countably infinite.

All mathematics demands is that things are well-defined. In that sense, infinite is just as meaningful as finite.

 

[gmax137]

It is already true in mathematics that the infinity symbol is not allowed to appear in any mathematical expression or equation.

I think that is overstating, see, e.g.

$$\frac \pi 4 = \sum_{k=0}^\infty \frac {(-1)^k} {2k+1}$$

Oops, it seems @jedishrfu beat me to this idea

 

[Mark44]

I think that is overstating,

I was tacitly assuming that "not allowed in equations" did not include limit expressions, limits of summations, or definite integral limits or the like.

 

[OmCheeto]

... zero certainly does[exist], as it accurately describes the number of pink flamingoes in my front yard. ...

What about fractional pink flamingo? If a pink flamingo were to die on your front lawn today, would it no longer be a pink flamingo? It might be a 'dead' pink flamingo, but that's just an added adjective. Just like we're all breathing in molecules of Caesar's last breath, IMHO, your front yard is littered with less than whole number pink flamingo.

But given the topic, and I'm not a mathematician; how do mathematicians deal with the fact that even though much of the universe is ruled logarithmically, there exists no 'zero' in logarithmic math?

as alway, OKTDIABMTAS

 

[FactChecker]

But given the topic, and I'm not a mathematician; how do mathematicians deal with the fact that even though much of the universe is ruled logarithmically, there exists no 'zero' in logarithmic math?

I would be more inclined to say that much of the universe is "ruled" exponentially and just presented or graphed logarithmically in order to compress an exponential result.

 

[gmax137]

as alway, OKTDIABMTAS

even google AI can't decipher that one for me

 

[OmCheeto]

even google AI can't decipher that one for me

OKTDIABMTAS = OK To Delete Infract And Ban, My Thoughts Are Saved

Did you never have a run-in with ZapperZ?
I was almost banned for the content of my very first post.

I still have no idea why I haven't been banned.
@Danger once said that my comments, while not scientifically correct, might make for a great science fiction novel. I'm going with that.

 

[berkeman]

Thread is done. Have a nice day.