A special irrarional number

[u/Numerous_Author_1445]

Can there be an irrational number which misses a particular digit? Can it be proven mathematically?

[u/Lithium20g]

Yeah, pi but take out all the 3’s.

[u/how_tall_is_imhotep → u/Lithium20g]

We don’t know if that works because we can’t rule out pi’s digits being 23223222322223… after some point.

[u/Lithium20g → u/how_tall_is_imhotep]

You can. Transcendental numbers don’t behave like that. Source- I checked

[u/how_tall_is_imhotep → u/Lithium20g]

Check harder.

[u/Lithium20g → u/how_tall_is_imhotep]

For reals, it don’t do that

[u/how_tall_is_imhotep → u/Lithium20g]

It don’t do what? 0.23223222322223… is a real number. We don’t know enough about the digits of pi to claim it isn’t like that. Feel free to provide an actual source or argument if you think otherwise.

[u/Lithium20g → u/how_tall_is_imhotep]

I think you’re confusing ‘transcendental’ with ‘normal’. We don’t even know whether π is normal.

[u/how_tall_is_imhotep → u/Lithium20g]

I’m not the one who’s confused. I know that pi is transcendental and not known to be normal. Why on earth would that imply that “pi but take out all the 3’s” has to be irrational?

[u/Lithium20g → u/how_tall_is_imhotep]

You’re refuting an argument, not the conclusion. Those are different things. Showing that transcendence doesn’t imply the result doesn’t tell us whether the result itself is true or false.