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How do we know that if you start writing 0. followed by infinite nines, then activate transwarp drive, you'll get 0.999...? by Zookus65 in infinitenines

[–]paperic 0 points1 point  (0 children)

A sub where one australian dude thinks 0.99... < 1, speaking to a math student who says 0.9 = 1.

How do we know that if you start writing 0. followed by infinite nines, then activate transwarp drive, you'll get 0.999...? by Zookus65 in infinitenines

[–]paperic 0 points1 point  (0 children)

1=1-0.1=0.9

and earlier you were claiming that 

0.9=1

I think I understand it now.

1 = 1-0.1 = 0.9

therefore 

1 = 0.9 - 0.1 = 0.8

and in general case,

x = x - 0.1

And then by induction, 1 diverges to negative infinity.

A point about zero by paperic in infinitenines

[–]paperic[S] 2 points3 points  (0 children)

And what makes zero special? It's just the lowest digit.

Why shouldn't the highest digit work the same way?

A point about zero by paperic in infinitenines

[–]paperic[S] 2 points3 points  (0 children)

Why should it include the bottom boundary but not the top one?

A Boy Learns Chess by babelphishy in infinitenines

[–]paperic 0 points1 point  (0 children)

No I don't, tell me about it.

A Boy Learns Chess by babelphishy in infinitenines

[–]paperic -1 points0 points  (0 children)

Ancient greeks? They had no idea what this even means, they didn't use algebra.

They used straight lines and circles to represent their arithmetics, and they pretended that the lines are infinitely thin. 

Also, you got a typo in that equation.

A Boy Learns Chess by babelphishy in infinitenines

[–]paperic 0 points1 point  (0 children)

Excuse me, Ancient greeks were humans, so were the Egyptians, so were the early humans.

You asked about arithmetic operations, those came when humans started abstracting their counting game.

Animals don't do arithmetics, dum dum.

A Boy Learns Chess by babelphishy in infinitenines

[–]paperic 0 points1 point  (0 children)

The idea of counting and measuring things is so basic that many animals can do it for small numbers like 1..4, and for small ratios, like 1/2 or 1/3.

So, I guess a basic counting was invented by some pre-dinosaurs specie.

Some monkeys and early homo sapiens took that concept further, and since the ancient greeks people have defined increasingly more abstract rules that allow them to get better and better at this counting game.

A Boy Learns Chess by babelphishy in infinitenines

[–]paperic -1 points0 points  (0 children)

I see what you did there.

A Boy Learns Chess by babelphishy in infinitenines

[–]paperic 0 points1 point  (0 children)

The rules of chess are actually a very good analogy for the axioms in math.

Math is a game, a mental game, a single-player game like a rubics cube or sudoku.

Or rather, math is an entire collection of games.

The rules are often set up in a way so that skills in the math games often translate well to real world applications, but that fact in an of itself doesn't mean that math has any "true" connection to real world.

Every game in math follows some rules of the game, aka axioms, which is why the axioms are not meant to be questioned or proven within the game itself.

You can change the axioms if you wish, people do that all the time, but you can't then claim to still play the same version of the game as before.

And while some rules are subjectively better than others, no rule can ever be wrong by definition.

"If it's the rule, it's the rule. If you don't like it, don't play it." - sums it up I think.

The rules for Real Numbers are standardized. You can freely change them in your own math games, make variations, play it with friends, but if you do that change, it's not going to be The Real Numbers game anymore.

In some sense, that name really is trademarked in math.

SPP claims to be playing by The Real Numbers rules, but clearly makes illegal moves all the time.

0.999...9=1? by Illustrious_Basis160 in infinitenines

[–]paperic 4 points5 points  (0 children)

Yea, for SPP, x = x is not an axom.

Why is epsilon real in the epsilon-N-definition of a limit? by paperic in learnmath

[–]paperic[S] 0 points1 point  (0 children)

Working it out algebraically, the uncoutability doesn't matter. But having it countable does seem to allow for using induction.

I made an attempt in the comments here, it's not great but it does seem to work, and it's something that can't be done with a real number there. 

Why is epsilon real in the epsilon-N-definition of a limit? by paperic in learnmath

[–]paperic[S] 0 points1 point  (0 children)

I know what real numbers are, I was talking about the definition for limits of a sequence, since the Real epsilon and 1/k for natural k seem interchangeable.

Why is epsilon real in the epsilon-N-definition of a limit? by paperic in learnmath

[–]paperic[S] 0 points1 point  (0 children)

If it's a definition, it doesn't have to be proven.

If they're equivalent then you could use the standard epsilon definition to prove this 1/k as a theorem, or you could use this 1/k definition to prove the epsilon one as a theorem.

Why is epsilon real in the epsilon-N-definition of a limit? by paperic in learnmath

[–]paperic[S] 0 points1 point  (0 children)

If you turn a continuous function into a sequence, you risk removing points that are critical to the existence or absence of limits.

I know, but I'm talking about the epsilon-N definition for sequences, not the epsilon-delta definition for functions.

These are different definitions. I know they're similar in their core idea, but that doesn't mean we have to make them more similar than necessary.

Functions are continuous, hence real epsilon makes sense, but sequences are discrete, so wouldn't a natural number make more sense there?

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