Is there an easy way to remember what '<' and '>' mean in maths?

Factual Questions
121

It doesn’t automatically mean that one side is bigger, one needs to be instructed in the concept, but the logic behind it is extremely straightforward. Large side, large value, small side, small value.

In what way could the small end of the symbol be linked with the larger value, that isn’t equally true the other way around?

It’s like with the King Kong pointing mnemonic. There is nothing inherent in the concept of King Kong, or a large being of any sort, pointing at something smaller than he is. It’s just as logical to have King Kong on the Empire State Building and all the small people pointing at it because it’s so big. It’s just as logical to say an alligator eats the small value, because only the small value will fit in its mouth.

Is there a logical way to look at the relative sizes of the symbol’s sides and link the pointy end to the large value and the wide end to the small value?

122

It may be a logic that was imposed as a mnemonic, in which case this is just an argument over the best mnemonic.

The equal sign was originally proposed in 1557 by Robert Recorde who stated that it represented two parallel lines “bicause noe 2 thynges, can be moare equalle.” Other mathematicians took up the idea, but some drew them vertically rather than horizontally. So = was explicitly stated to be a symbolic reference to an abstract geometric property.

Thomas Harriot first proposed symbols for “strictly greater than” and “strictly less than”. I’m not sure why “strictly” was necessary, but others also used that phrase when discussing the symbols. According to ehow:

And wikipedia says that he developed his signs from Algonquian symbols. Aha. The actual Algonquian symbol ishere, as are Harriot’s original symbols, which look like claws. Sadly, the cite does not specify which symbol was which. But in any case the three symbols were not created together as part of a logical set.

It’s an anthropomorphic, imaginary alligator. Everything is smaller than it is and it has a human’s thought processes and tendency to grab the biggest cookie.

Yes. Once it becomes part of one’s mnemonic or categorization for the concept, which is which is self-evident. But we learn what an arrow (symbol) is long before that. So whether we remember or not, the first thing that we though when we saw < or > was that it was an arrow, pointing a direction. That’s a totally different category of symbol and the category has to be actively overwritten in order to remember “greater than” or “less than” correctly.

The easiest way to overwrite that categorization or association will depend on the individual. Until the " ====> [here it is!]" association is overwritten for a mathematical context, it will remain the default association and will confuse.

123

Exactly.

It’s obviously confusing to many people. Just google it and you’ll see it’s not obvious to everyone. To me, it’s just divergent or convergent lines. Whether you think of it as WIDE-means-BIG to pointy-means-small or visualize it as a mouth eating the bigger number, what’s the difference? In both cases, you are using a visualization. After synthesizing the visualization and using it, it becomes second nature and you don’t have to rely on it. But I still think CHOMPCHOMP the bigger number. That’s the visualization that sticks to me. I fully understand the other one, but it’s not as “sticky” to me. Why is it so difficult to understand that people have different ways of learning concepts? For example, I never had to memorize Every Good Boy Does Fine or FACE to learn my musical staff. I just memorized it and that was that. It seemed easy enough for me to do. But some people require a crutch to learn it or to double check their work. Eventually, they also learn it instinctively. What’s wrong with that?

You’re already making assumptions for how to look at the symbol. You’re seeing bigger and smaller. I’m not. I’m seeing, naturally, something that points. If I want to get from 2 to 5 on the number line, which way do I go? > of course. If I want to get from 5 to 2 on the number line, which way do I go? < of course. You’re stuck in one interpretation of the symbol, because that’s the interpretation you were taught. If Harriot (actually, Harriot didn’t use that symbol, I believe it came in another work, IIRC) decided to go with “pointing” method, we’d all be here arguing: duh, it’s obvious! 5 is farther to the right on the number line, so 2 > 5, as in 2 –> 5. How could you think anything else? You so dumb!

There is nothing inherently more logical to me about two lines converging meaning larger-to-smaller than using the symbol as an arrow (a very familiar symbol) meaning in which direction you have to go along the number line to reach one number vs. the other.

It seems we are going to have to disagree on that last point. That’s fine with me. The fact of the matter is that it IS confusing for many people, it is NOT immediately obvious, and some people are aided by learning to visualize it–whether it is your way (wide apart lines mean big, point at the end means small), or a greedy, hungry alligator or Pac Man eating the bigger number. The end goal is to educate. I don’t care how you’re taught, but not everyone thinks the same way, so it’s not dumb to find different ways to teach.

And that’s the last I care to say about it. I’ve made my point enough here and clear enough here. If you disagree, that’s fine by me.

124

Right you are (I was mistaken over the meaning of the term). Nevertheless, one seems less silly than the other.

125

I can’t help that you feel that way.

126

Can someone please tell me how to remember whether the alligator eats the bigger number or the smaller number please?

127

And while you’re at it, how do I remember if it’s an alligator or a crocodile?

128

easy! <rocodile and alliga>or . as you can see, the number of letters on either side of the word also indicates which side is greater/lesser than.

129

I remember at age around seven coming up with the crocodile mnemonic by myself. I am not opposed to memory devices per se. I think they can be useful. And generally speaking, the more ridiculous the image the better it sticks in the mind.

The difference is that I arrived at the mental image by myself as I processed the concept and considered how I would remember it.

I don’t think spouting mnemonics is a useful teaching tool for the most part. We should teach principles and concepts. We should teach notation and conventions. If, once the concept is established there is a difficulty in memorising notation or terminology, then the mnemonic comes into play. And ideally, it is the student’s own mnemonic so that it is memorable to that student. In cases like this where the concept is neatly encapsulated in the notation I would think that teaching about crocodiles gorillas arrows or music playback devices is couterproductive – adding a layer of complexity and obfuscating the foundational principles.

Where mnemonics are useful is for lists (especially those that need to be in order), and naming/signing conventions that are arbitrary to begin with.
[ul]
[li]I think the right hand slap rule for orthogonal force, current and electric field is helpful.[/li][li]The alliteration of population parameters sample statistics is likewise helpful.[/li][li]I teach my students that they should all have a way of memorising the first 20 elements on the periodic table and teach “positive proton, neutral neutron”.[/li][li]I have a melodic mnemonic for the alphabet (both forwards and backwards) and you do too in all likelihood if you watched Sesame Street.[/li][li]I get my students to physically point with their fingers when learning to multiply matrices so that they get the feel of one finger going across and the other going down.[/li][/ul]
The crux is this: the principle comes first and the mnemonic is to deal with the representation. In the case of “<” I would consider that the principle is sufficiently entrenched in the notation that no other prompting should be needed. And if it is needed then it should originate in the student’s own attempts to organise their understanding and not as an imposition originating from the teacher.

130

Upon rereading the OP, it’s not clear that their confusion is about which value is bigger or smaller as it relates to the symbol, but rather (and I can’t believe that only a few have touched on this over three pages) what are the names for the symbols.

I think s/he and probably most other people have a more or less intuitive understanding that the littler side of the symbol points to the smaller value, and that the bigger side of the symbol points to the larger value. The question, it seems to me, is what is the name for “<” and what is the name for “>”. Since flipping over a statement of inequality doesn’t affect its truth (e.g., “5>2” is equivalent to “2<5”), it’s not necessarily obvious which symbol is named what (note: named what, not means what (which seems to be what almost everyone is addressing)), especially if you don’t come from a culture which reads left-to-right.

So Doctor Why Bother, if you’re still with us, read TonySinclair’s post, #5, and ignore everything else; he gives probably the simplest English mnemonic to remember what the symbols are named–not what they mean–which is what I think you were looking for in the first place.

131

Or not.

132

I have never heard that before -

I created one to help my nephew remember the same thing
My Very Excellent Mother Jumps Suddenly Up Naked…

Not exactly the epitome of elegant or grammatically correct english - but he remembered it. (as is my 9 year old daughter)

133

The version I heard as a kid was “My very educated mother just served us nine pizzas”. Never mind the fact that the pizzas are gone now, and that when I was a kid the pizza was actually before the nine.

134

I even learned a mnemonic (circa 3rd grade I think?) for remembering how to spell Arithmetic:
A Rat In The House May Eat The Ice Cream.
That one stuck with me to this day. Must have been one damn good mnemonic.

And there are several mnemonics around for remembering the seven levels of the Internet Protocol stack, in both directions.
Please Do Not Throw Sausage Pizza Away
All People Seem To Need Data Processing
And various others

135

Aha! I’ve seen that symbol many a time, and never really knew what it meant! Thanks, Mangetout. Total Ignorance in Universe just reduced!

ETA: So, has anyone mentioned yet the mnemonic for remembering resistor color codes?
Bad Boys Rape Our Young Girls, But Violet Gives Willingly.
(Back in the day, when it was allowed to teach things like that.)

136

But which B is black and which is brown? :slight_smile: My brain just lops that one as “black, brown, colors of the rainbow (minus indigo), grey, white.” It always just kind of made sense to me. Though like I said before, different people have different ways of making it “stick” to their memory. The biggest problem for me with resistors is just being able to discern the color on the damn things when dealing with the tiny type (1/4 watt or 1/8 watt…I can’t remember. Red and orange can get a bit difficult for me at those sizes.)

137

This is what I was taught. He wants to eat the bigger one. Of course, this lets everyone know the approximate years we were in grade school.

138

nm

139

That’s why I learned the even more offensive one that goes “Black Bastards Rape Our Young Girls…”, and then it’s easy to remember that black comes first.

You can drag in homophobia too by ending it “But Poofs Go Without” (Purple). :eek:

One mnemonic I refuse to surrender is this:

Now I - even I - would celebrate
In rhymes unapt the great
Immortal Syracusan rivaled nevermore
Who in his wondrous lore
Passed on before
Gave men his guidance how to circles mensurate

which wretched piece of doggerel has stuck with me for even more years than the number of digits of p that it ciphers.

140

I’m imagining a 3rd grade teacher writing <rocodile and alliga>or on the chalk board and explaining it to her class that way. The kids are all WTF?. :slight_smile:

Now your educated mother serves U nothing!