Unit 17 More Signs of Comparison and Operation,

and Other Special Symbols

# More Signs of Comparison

The following signs are some more commonly used signs of comparison. Remember that signs of comparison require a space on either side of the comparison sign regardless of the print spacing (except with a grouping sign, indicator, or other sign of punctuation).

Less than or equal to ≤ | ⠐⠅⠱ |

Greater than or equal to ≥ | ⠨⠂⠱ |

Similar to ∼ | ⠈⠱ |

Approximately Equal to ≈ | ⠈⠱⠈⠱ |

Congruent to ≅ | ⠈⠱⠨⠅ |

Ratio ∶ | ⠐⠂ |

Proportion (as) ∷ | ⠰⠆ |

Therefore ∴ | ⠠⠡ |

*Note: Examples that are not embedded in UEB have omitted the Nemeth Code switch indicators.*

# Examples for ≤ and ≥:

35 __ 3^{3 }(≤ or ≥)

⠼⠒⠢⠀⠤⠤⠤⠤⠀⠼⠒⠘⠒⠀⠷⠐⠅⠱⠀⠕⠗⠀⠨⠂⠱⠾

q ≥ 25

⠟⠀⠨⠂⠱⠀⠼⠆⠢

# Examples for ∼, ≈, ≅:

x∼y

⠭⠀⠈⠱⠀⠽

$\u25b5\mathrm{D}\mathrm{E}\mathrm{F}\sim \u25b3\mathrm{M}\mathrm{N}\mathrm{O}$⠫⠞⠀⠠⠙⠠⠑⠠⠋⠀⠈⠱⠀⠫⠞⠀⠠⠍⠠⠝⠠⠕

π ≈ 3.14

⠨⠏⠀⠈⠱⠈⠱⠀⠼⠒⠨⠂⠲

1 in. ≈ 2.5 cm.

⠼⠂⠀⠊⠝⠲⠀⠈⠱⠈⠱⠀⠼⠆⠨⠢⠀⠉⠍⠲

∠GHI ≅ ∠PQR

⠫⠪⠀⠠⠛⠠⠓⠠⠊⠀⠈⠱⠨⠅⠀⠫⠪⠀⠠⠏⠠⠟⠠⠗

* Notice that a space is left after the angle symbol because it is a shape, even though there is no space in the print version.

# Ratio and Proportion

Ratio and proportion are comparisons of two numbers. Although print uses the punctuation "colon" for ratio and two colons for proportion, Nemeth Code considers ratio and proportion mathematical symbols and the punctuation colon is not used. Ratios and proportions written between Nemeth Code indicators must use Nemeth Code ratio and proportion symbols.

# Examples:

Ratio 5:4

⠠⠗⠁⠞⠊⠕⠀⠼⠢⠀⠐⠂⠀⠼⠲

Ratio of dogs/cats is 3:2

⠠⠗⠁⠞⠊⠕⠀⠷⠀⠙⠕⠛⠎⠸⠌⠉⠁⠞⠎⠀⠊⠎⠀⠸⠩⠀⠼⠒⠀⠐⠂⠀⠼⠆⠀⠸⠱

When two ratios are equivalent, the sign for proportion or "as" is used rather than the equal sign.

# Examples:

a:b :: c:d

⠁⠀⠐⠂⠀⠃⠀⠰⠆⠀⠉⠀⠐⠂⠀⠙

Mixture: 0.5:4 :: 3:?

⠠⠍⠊⠭⠞⠥⠗⠑⠒⠀⠸⠩⠀⠼⠴⠨⠢⠀⠐⠂⠀⠼⠲⠀⠰⠆⠀⠼⠒⠀⠐⠂⠀⠿⠀⠸⠱

# Therefore

The "therefore" symbol is a way to make a comparison statement about two things and, like all signs of comparison, requires a space on either side.

# Examples:

a=b ∴ a^{2}=b^{2}

⠁⠀⠨⠅⠀⠃⠀⠠⠡⠀⠁⠘⠆⠀⠨⠅⠀⠃⠘⠆

E = F ∴ F = E

⠠⠑⠀⠨⠅⠀⠠⠋⠀⠠⠡⠀⠠⠋⠀⠨⠅⠀⠠⠑

# Comparison Signs with Negation

All comparison signs may be negated by a slash or vertical stroke in print. In Nemeth Code, the simple slash (dots 3-4) is placed unspaced in front of the comparison symbol it negates.

Slash for Negation | ⠌ |

# Commonly Negated Signs

Not equal ≠ | ⠌⠨⠅ |

Not greater than≯ | ⠌⠨⠂ |

Not less than≮ | ⠌⠐⠅ |

Not Parallel to ∦ | ⠌⠫⠇ |

# Examples:

$30\%\ne {\displaystyle \frac{1}{3}}$⠼⠒⠴⠈⠴⠀⠌⠨⠅⠀⠹⠂⠌⠒⠼

EF ∦ GH

⠠⠑⠠⠋⠀⠌⠫⠇⠀⠠⠛⠠⠓

5x ≯ 10

⠼⠢⠭⠀⠌⠨⠂⠀⠼⠂⠴

Triangle abc ≇ Triangle def

⠸⠩⠀⠠⠞⠗⠊⠁⠝⠛⠇⠑⠀⠁⠃⠉⠀⠌⠈⠱⠨⠅⠀⠠⠞⠗⠊⠁⠝⠛⠇⠑⠀⠙⠑⠋⠀⠸⠱

Evaluate; p = q, but q ≠ r.

⠠⠑⠧⠁⠇⠥⠁⠞⠑⠆⠀⠸⠩⠀⠏⠀⠨⠅⠀⠟⠠⠀⠠⠄⠃⠥⠞⠀⠟⠀⠌⠨⠅⠀⠗⠀⠸⠱⠲

# Combined Signs of Operation (Plus Minus)

Print material often combines plus/minus or minus/plus into one sign of operation. In Nemeth Code plus/minus or minus/plus appear horizontally unspaced from their related term(s) and are considered one operation.

Plus or minus ± | ⠬⠤ |

Minus or plus ∓ | ⠤⠬ |

# Examples:

x±5

⠭⠬⠤⠢

5∓4 = y

⠼⠢⠤⠬⠲⠀⠨⠅⠀⠽

$\sqrt{225}=\pm 15$⠜⠆⠆⠢⠻⠀⠨⠅⠀⠬⠤⠼⠂⠢

3 ft = ±1 m

⠼⠒⠀⠋⠞⠀⠨⠅⠀⠬⠤⠼⠂⠀⠰⠍

When plus and/or minus signs are combined horizontally in print, one after the other, the multipurpose indicator must be used to separate the signs in braille.

Plus minus +- | ⠬⠐⠤ |

Minus plus -+ | ⠤⠐⠬ |

Minus minus - - | ⠤⠐⠤ |

# Examples:

+4-+5

⠬⠼⠲⠤⠐⠬⠢

-7+-5

⠤⠼⠶⠬⠐⠤⠢

3 - -4

⠼⠒⠤⠐⠤⠲

* Note: Do not divide plus/minus between lines.

# Brain Boost

When the asterisk, pound sign (aka crosshatch, hashtag), or ampersand are used in mathematical context, they are considered a sign of operation and the Nemeth Code symbols for asterisk, pound, and ampersand must be used unspaced from their related term(s).

Asterisk * | ⠈⠼ |

Pound/Hashtag # | ⠨⠼ |

Ampersand & | ⠸⠯ |

# Examples:

A&B

⠠⠁⠸⠯⠠⠃

x#y

⠭⠨⠼⠽

D∗E

⠠⠙⠈⠼⠠⠑

Z* = conjugate of Z.

⠸⠩⠀⠠⠵⠈⠼⠀⠨⠅⠀⠸⠱⠀⠒⠚⠥⠛⠁⠞⠑⠀⠷⠀⠰⠠⠵⠲

The Nemeth asterisk and pound sign (rather than the literary sign) must be used when they appear in mathematical context, even when they are used simply for reference.

# Example:

*See note A

⠈⠼⠠⠎⠑⠑⠀⠝⠕⠞⠑⠀⠰⠠⠁

A numeric indicator must be used for a number that follows a Nemeth asterisk or pound sign.

# Examples:

*274*

⠈⠼⠼⠆⠶⠲⠈⠼

* Notice how the numeric indicator is placed after the first *, otherwise the dot 4 would be read as typeform: script and read (script)##274*.

#5

⠨⠼⠼⠢

* Notice how the numeric indicator is placed after the #, otherwise the dots 4-6 would be read as typeform: italics and read (italics)##5.

# Examples within Nemeth Code switch indicators

Five #10 bags = $25.

⠠⠋⠊⠧⠑⠀⠸⠩⠀⠨⠼⠼⠂⠴⠀⠠⠄⠃⠁⠛⠎⠀⠨⠅⠀⠈⠎⠆⠢⠀⠸⠱⠲

Size of set; #{4,6,8} = 3

⠠⠎⠊⠵⠑⠀⠷⠀⠎⠑⠞⠆⠀⠸⠩⠀⠨⠼⠨⠷⠲⠠⠀⠖⠠⠀⠦⠨⠾⠀⠨⠅⠀⠼⠒⠀⠸⠱

Calculate 2*2*2 = ?

⠠⠉⠁⠇⠉⠥⠇⠁⠞⠑⠀⠸⠩⠀⠼⠆⠈⠼⠼⠆⠈⠼⠼⠆⠀⠨⠅⠀⠿⠀⠸⠱

# @ Sign

The Nemeth "at sign" is treated as a sign of comparison. Except for punctuation, indicators, or related symbols of grouping, a space must be left on both sides of the @ symbol.

"At sign" @ | ⠈⠁ |

# Examples:

4 boxes @ 27¢ = $1.08.

⠼⠲⠀⠃⠕⠭⠑⠎⠀⠈⠁⠀⠼⠆⠶⠈⠉⠀⠨⠅⠀⠈⠎⠂⠨⠴⠦⠸⠲

15# (@ $10)

⠼⠂⠢⠨⠼⠀⠷⠈⠁⠀⠈⠎⠂⠴⠾

* Notice there is no space after the parenthesis.