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I predict that this post will get approximately 01000011100101100000000000000000 upvotes (lemmy.world)

submitted 3 days ago* (last edited 3 days ago) by [email protected] to c/[email protected]

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[–] [email protected] 1 points 3 days ago (2 children)

But some irrational numbers are only so in base 10

[–] [email protected] 9 points 3 days ago (1 children)

What? That's not true at all...

[–] [email protected] 3 points 3 days ago (5 children)

Base π: π=1

[–] [email protected] 6 points 3 days ago

Writing the same number a different way does not make it rational. There are no two natural numbers p and q so that p/q = 1 base pi.

[–] [email protected] 5 points 3 days ago

Even in base π, π is still considered an irrational number; using an irrational based doesn't change the fundamental identity of whole numbers or irrational numbers, it just changes the way we write them.

[–] [email protected] 2 points 2 days ago* (last edited 2 days ago)

1 is always 1. It's 1 × b⁰ where b is the base. Anything raised to the zeroth power is 1.

10 is the base. 1 × b¹ + 0 × b⁰

[–] [email protected] 3 points 3 days ago* (last edited 3 days ago)

That doesn't make it rational but simply makes it writable in 2 digits(10)

Also you should have 3.1415... "number of characters" in that base... The base becoming irrational will make the number irrational

[–] [email protected] 2 points 3 days ago

π = 10

in base 10, 10 = 10.

[–] [email protected] 3 points 3 days ago* (last edited 3 days ago)

Kinda. Technicaly no since an irrational number is a number that cannot be defined as a ratio of 2 existing rational numbers. Any number that can be represented in any rational base can by definition be represented as a ratio of somthing/base^n. This ignore the case of an irrational base but its practically useless cos any rational and most other irrational numbers will be irrational.

What u think ur trying to say is that some numbers cannot be represented in one base but can in another for example 1/3 can be represented as a decimal in base 3 but cannot jn base 10 ie u get 0.333(3 repeating forever).

Tieing back to floating point which uses base 2 u end up with simmillar issues with base10 base2 conversions hence most of the errors with floating point errors (yes at very large and very small numbers u lose accuracy but in practice most errors arise from base convention).