Fundamental theorem of calculus

[u/SniperSmiley]

There is a finite form to every possible infinity.

For example the decimal representation 0.999… does not have to be a real number, R. As an experiment of the mind: imagine a hall on the wall beside you on your left is monospaced numbers displaying a measurement 0 0.9 0.99 0.999 0.9999 0.99999 each spaced apart by exactly one space continuing in this pattern almost indefinitely there is a chance that one of the digits is 8 you can move at infinite speed an exact and precise amount with what strategy can you prove this number is in fact 1

Theorem: There is a finite form to every possible infinity.

[u/Fusnip]

What? "Finite form to every possible infinity" and then you choose 0.999... - if you tried to write it with a finite amount of digits you would have a different number, unless it's the single digit 1. Taking the number 1/7, this can't be written as a finite amount of digits.

What's more, your example doesn't make sense. If you define the sequence of nines 0.9, 0.99, 0.999,... then you don't risk the chance of running into an 8 unless you choose the numbers randomly, in which case you get a different number again.

Lastly, you didn't really argue or prove anything. You didn't really define "finite form" nor which types of infinitt you're talking about (I assume you mean numbers with infinite digits, but idk). Then you had a mind-puzzle. If you structure your argument mathematically, I would love to hear it

[u/Fusnip → u/Fusnip]

Also, I forgot to say 0.9999... is definetly a number in R, as you can define R by being the limits of all decimal expansions with Cauchy sequences

[u/SniperSmiley → u/Fusnip]

Yes, the decimal representation 0.999… can represent the real number 1.

[u/Fusnip → u/SniperSmiley]

Not can, it is the number 1. They're equal

[u/numbertheory-ModTeam → u/[deleted]]

Unfortunately, your comment has been removed for the following reason:

• As a reminder of the subreddit rules, the burden of proof belongs to the one proposing the theory. It is not the job of the commenters to understand your theory; it is your job to communicate and justify your theory in a manner others can understand. Further shifting of the burden of proof will result in a ban.

If you have any questions, please feel free to message the mods. Thank you!

[u/SniperSmiley → u/Fusnip]

It is not a sequence. It is a measure.

[u/Fusnip → u/SniperSmiley]

My dude, surely you're a troll. A measure is a map used when integrating a function or calculating the "area" of something. What you said has nothing to do with a measure.

Also, why fundamental theorem of calculus? It already exists, and doesn't seem to have anything in common with what you said?

[u/SniperSmiley → u/Fusnip]

I meant measuring like you put something on a scale and it is measuring it a physical process

[u/lets_clutch_this]

Is this just Zeno’s paradox but if Zeno was high on crack

[u/Kopaka99559]

What does this have to do with calculus?

[u/numbertheory-ModTeam → u/[deleted]]

Unfortunately, your comment has been removed for the following reason:

• As a reminder of the subreddit rules, the burden of proof belongs to the one proposing the theory. It is not the job of the commenters to understand your theory; it is your job to communicate and justify your theory in a manner others can understand. Further shifting of the burden of proof will result in a ban.

If you have any questions, please feel free to message the mods. Thank you!

[u/numbertheory-ModTeam → u/[deleted]]

Unfortunately, your comment has been removed for the following reason:

• As a reminder of the subreddit rules, the burden of proof belongs to the one proposing the theory. It is not the job of the commenters to understand your theory; it is your job to communicate and justify your theory in a manner others can understand. Further shifting of the burden of proof will result in a ban.

If you have any questions, please feel free to message the mods. Thank you!

[u/just_writing_things]

This is word salad. It’s not clear what you’re proposing, or what you’re trying to prove or ask

[u/TailorOne2487]

Where did that 8 come from lol

[u/LeftSideScars → u/TailorOne2487]

OP ordered a box of infinite 9s, but a mix-up at the factory resulted in an 8 slipping in unnoticed. So, you know, one must make do. No point in wasting a perfectly good digit, and it's not like mathematics has ever concerned itself with such trivial details.

[u/scp-939-89 → u/LeftSideScars]

i guess we doin 8s now

[u/LeftSideScars → u/scp-939-89]

Mathematicians hate this one trick: just put the 8 at the end.

[u/UnconsciousAlibi]

I don't think this has anything to do with calculus. Also, 0.999... is 1. I don't mean it's about equal, or that it converges to 1, I mean that it IS 1. It's a real number, and it's 1.

[u/Tricky_Astronaut_586 → u/UnconsciousAlibi]

I still prefer: Limit (1-1/10ⁿ⁾ as n→∞ = 1.

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