What number comes after 0.10? 0.2 or 0.11?

Question

What number comes after 0.10? 0.2 or 0.11? Decimal realm is confusion for me, help:)

Rational (or real) numbers do not have immediate successors unless we pick a strange ordering. — Tobias Kildetoft, Nov 03 '13 at 17:54
And this isn't unique to $\mathbb{R}$. Given a rational number there's no next rational either. — Malice Vidrine, Nov 03 '13 at 17:58
If $p$ is some rational number bigger than $0.10$, then we can always fit another rational number $q$ between $p$ and $0.10$ by defining $q = \frac{0.10 + p}{2}$. This may give you some insight as to why there is no notion of 'next biggest number' for the rationals — tylerc0816, Nov 03 '13 at 17:58
nice helps! Seems like circular logic also have big advantages. — , Nov 03 '13 at 18:02
@Tobias the back and forth fluctuations from 0 to 1 is a fluctuation. While Natural numbers are straight fall into infinity. Shouldnt this be also applied to decimal point numbers i.e, a straight fall into zero. The addition + operator is 'as is' in decimal point numbers while the multiplication * gives you a small number which is contrary to natural numbers. — , Nov 03 '13 at 18:22
@Tobias I am present within the number line between 0 and 1:) — , Nov 03 '13 at 18:34

score 2 · Accepted Answer · answered Nov 03 '13 at 18:05

2

There is no immediate successor of $0.1$ within the real (or rational) numbers; just take numbers like

\begin{align*} &0.1 \\ &0.01 \\ &0.001 \\ &0.0001 \\ &\vdots \end{align*}

What we can say, however, is that

$$0.1 < 0.11 < 0.2$$

This is because the first number represents $10$ parts of $100$, the next represents $11$ parts, and the third represents $20$ parts.

answered Nov 03 '13 at 18:05

don't you think that an axiomatic amendenment is required then? – Nov 03 '13 at 18:12
1

@WaqarAhmad No. Immediate successors aren't terribly useful in this context, and there's no need for them. – Nov 03 '13 at 18:13

1 Answers1