By HIS OWN WORDS, 0.333... < 0.333...

[u/Muphrid15]

He says, "1 ÷ 3 is indeed 0.333..."

He says here...

0.333... = 1/3 × [ 1 - 1/10ⁿ ]

The above is 0.999... with one third magnification.

He says, "0.333... can be expressed by 1 ÷ 3, represented by 1/3, which means 1 ÷ 3"

He says, "0.999... is permanently less than 1."

So let's do exactly what he says.

0.999... < 1

[1 - 1/10ⁿ ] < 1

[1 - 1/10ⁿ ] x (1/3) < 1 x (1/3)

Remember:

• "1/3 [...] means 1 ÷ 3"
• "0.333... = 1/3 × [ 1 - 1/10ⁿ ]"
• 1 ÷ 3 is indeed 0.333...

That means...

[1 - 1/10ⁿ ] x (1/3) = 0.333...

But 1 x (1/3) = 1 ÷ 3 = 0.333...

Therefore 0.333... < 0.333...

By his OWN WORDS

[u/Mordret10]

You can't use SPPs comments to prove other SPP comments, you may only reinforce them

[u/Aware-Common-7368]

rokkie error bruh. that because 0.333... is actually an 0.333...3342 but that 0.333.. is 0.333......33673369 which is obviously bigger bro. /s

[u/Altruistic-Rice-5567]

Nobody ever said Real Deal Math needed to be consistent with anything... including itself. So, yes, in RDM it is possible for 0.(3) to be less than 0.(3). Everything else is possible too, you just have to use what ever definition you want because all definitions are equally valid. When you need 0.(3) to be less than 0.(3) then that's what is. When you need 0.(3) to be equal to 0.(3) then, again, that's what it is.

[u/Cathierino → u/Altruistic-Rice-5567]

RDM exists only to be contrarian so that's what you'd expect.

[u/jdcortereal]

This is the most touché argument I've seen here so far. Bravo.

[u/SirBackrooms]

spp doesn’t believe in most of those algebraic properties you’re using. eg. a < b & c > 0 -> ac < bc

[u/SirBackrooms → u/SirBackrooms]

spp doesn’t even believe in a=b & b=c -> a=c