# What does the sign that looks like $\geq$ except with the bottom line being sloped mean?

I'm referring to this symbol: $\geqslant$.

No symbol list I've come across mentions it. I saw it in the book Pattern Recognition and Machine Learning by Christopher M. Bishop.

## migrated from cs.stackexchange.comFeb 18 '15 at 8:15

This question came from our site for students, researchers and practitioners of computer science.

• It is precisely the same thing as ≥. – Jukka Suomela Feb 16 '15 at 20:39
• The difference is in the font. – Dave Clarke Feb 16 '15 at 21:18
• @DaveClarke They are actually two different symbols, ≤ (Less-Than or Equal To) and ⩽ (Less-Than or Slanted Equal To). – Raphael Feb 17 '15 at 7:52
• @JukkaSuomela, thanks for the clarification. I will edit this question back to the original. – Joel Reyes Noche Feb 18 '15 at 8:49

An example of the symbol's context can be found on p19 of Bishop - Pattern Recognition and Machine Learning:

\qquad\begin{align*} p(x) &\geqslant 0 \\ \int p(x)\,\mathrm{d}x &= 1 \end{align*}

The symbols $\geq$, $\geqslant$ and >=, all mean the same thing: Greater than or equal to.

The same applies to its converse: $\leq$, $\leqslant$ and <=, all mean: Less than or equal to.

Context for the latter symbol:

$\qquad\displaystyle f\left(\sum_{i=1}^M \lambda_i x_i\right) \leqslant \sum_{i=1}^M \lambda_i f(x_i)$

The differences can be attributed to the character set available, and/or the particular font that is used. In this particular book, the author specifies, on page viii, than they have used $\LaTeX$.

• Every reasonable mathematics font will have both; usage is a matter of personal, stylistic choice. – Raphael Feb 17 '15 at 7:53
• Certain hardware platforms may not though. The ASCII character set does not have these characters. – Greenonline Feb 17 '15 at 8:01
• @Greenonline ASCII doesn't even have $\leq$. – David Richerby Feb 17 '15 at 9:38
• Exactly, hence the composite >= and <= characters... :-) – Greenonline Feb 17 '15 at 9:42
• @Greenonline If you (have to) use this outside source code, something is terribly wrong. – Raphael Feb 18 '15 at 8:15