Question

Is there a valid proof of one-to-one correspondence b/n the real interval $(0, 1]$ and the nonterminating decimal expansions $0.d_1 d_2 d_3 …$?

score 128 · Answer 1 · 2022-06-12 02:23:39

128

Views

Is there a valid proof of one-to-one correspondence b/n the real interval $(0, 1]$ and the nonterminating decimal expansions $0.d_1 d_2 d_3 …$?

Published on 12 Jun 2022 - 2:23

score 186 · Answer 2 · 2022-06-18 17:47:34

186

Views

How to show that there are no decimal representations of $1$ other than $1.000\dots$ and $0.999\dots$?

Published on 18 Jun 2022 - 17:47

score 149 · Answer 3 · 2022-06-20 19:28:16

149

Views

Proving that a real number has at most two decimal expansions

Published on 20 Jun 2022 - 19:28

score 26 · Answer 4 · 2026-03-30 17:17:24

26

Views

some decimal numbers with fractional part that can be written down easily in base 10 cannot be in base 2 without using infinite series of number(0.2)

Published on 30 Mar 2026 - 17:17

score 130 · Answer 5 · 2022-07-10 19:06:15

130

Views

Find all integers $x$ that are at most $100000$ so that $S(11x) = x$.

Published on 10 Jul 2022 - 19:06

score 198 · Answer 6 · 2022-07-12 22:27:08

198

Views

Is there a formula that allows you calculate the n-th decimal digit of pi without calculating the previous digits?

Published on 12 Jul 2022 - 22:27

score 69 · Answer 7 · 2022-07-15 12:14:59

Given any two normal numbers, can we always find a find a truncation point at which the digits can be rearranged from one to the other?

score 113 · Answer 8 · 2022-08-01 16:10:17

113

Views

Test of rational number as a terminating decimal number using $2^m \cdot 5^n$

Published on 01 Aug 2022 - 16:10

score 88 · Answer 9 · 2022-08-11 19:40:40

88

Views

Decimal Expansions - Pugh Exercise 1.18

Published on 11 Aug 2022 - 19:40

score 54 · Answer 10 · 2022-08-15 07:43:54

54

Views

Find, in terms of $\epsilon$, the smallest positive integer $n$ such that $|\sqrt{n}-\lfloor{\sqrt{n}}\rfloor-\frac12|<\epsilon$.

Published on 15 Aug 2022 - 7:43

score 1.8k · Answer 11 · 2026-03-25 20:11:16

1.8k

Views

Can you prove that proof-by-induction is invalid for the real interval [0, 1]?

Published on 25 Mar 2026 - 20:11

score 163 · Answer 12 · 2026-03-28 06:24:03

163

Views

Can we define addition of numbers which are NOT eventually all zero as we go to the left?

Published on 28 Mar 2026 - 6:24

score 542 · Answer 13 · 2022-08-22 01:14:50

542

Views

Surprising Patterns in Numbers whose Digit Sum is equal to their Square Root in an arbitrary Base.

Published on 22 Aug 2022 - 1:14

score 66 · Answer 14 · 2022-08-23 13:57:51

66

Views

In how many ways can 3 distinct numbers fill 6 blanks (each repeated exactly twice)?

Published on 23 Aug 2022 - 13:57

score 73 · Answer 15 · 2022-08-24 21:53:14

73

Views

Digit sum formula $n - 9 \sum_{i\ge1} \left \lfloor \frac{n}{10^i} \right \rfloor$

Published on 24 Aug 2022 - 21:53

List Question

Is there a valid proof of one-to-one correspondence b/n the real interval $(0, 1]$ and the nonterminating decimal expansions $0.d_1 d_2 d_3 …$?

How to show that there are no decimal representations of $1$ other than $1.000\dots$ and $0.999\dots$?

Proving that a real number has at most two decimal expansions

some decimal numbers with fractional part that can be written down easily in base 10 cannot be in base 2 without using infinite series of number(0.2)

Find all integers $x$ that are at most $100000$ so that $S(11x) = x$.

Is there a formula that allows you calculate the n-th decimal digit of pi without calculating the previous digits?

Given any two normal numbers, can we always find a find a truncation point at which the digits can be rearranged from one to the other?

Test of rational number as a terminating decimal number using $2^m \cdot 5^n$

Decimal Expansions - Pugh Exercise 1.18

Find, in terms of $\epsilon$, the smallest positive integer $n$ such that $|\sqrt{n}-\lfloor{\sqrt{n}}\rfloor-\frac12|<\epsilon$.

Can you prove that proof-by-induction is invalid for the real interval [0, 1]?

Can we define addition of numbers which are NOT eventually all zero as we go to the left?

Surprising Patterns in Numbers whose Digit Sum is equal to their Square Root in an arbitrary Base.

In how many ways can 3 distinct numbers fill 6 blanks (each repeated exactly twice)?

Digit sum formula $n - 9 \sum_{i\ge1} \left \lfloor \frac{n}{10^i} \right \rfloor$

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