Comparison operators — ==, !=, - , - , - =, - =

WHAT they are

Definition Comparison (relational) operators

Operators that compare two operands and return a Boolean (True/False).

Operator	Reads as	`True` when…
`==`	equal to	both sides have the same value
`!=`	not equal to	the sides differ
`<`	less than	left is smaller
`>`	greater than	left is larger
`<=`	less than or equal	left ≤ right
`>=`	greater than or equal	left ≥ right

Common mistake

= is NOT == Why the wrong idea feels right: In maths, = means "equals". So x = 5 looks like a question "is x five?". The truth: In Python = is assignment (put 5 into x). The question "is x five?" is x == 5. The fix: One = changes a variable; two == checks a variable.

x = 5      # assignment: store 5
x == 5     # comparison: True

Bonus: if x = 5: raises a SyntaxError, which is Python protecting you.

HOW the answer is built (derivation from first principles)

A comparison isn't magic — it reduces to one fundamental idea: ordering / identity of values.

Step 1 — the only primitive we truly need is < (less-than). Why? Because every other comparison can be defined using < plus logical NOT and equality:

\begin{aligned} a > b &\equiv b < a \\ a \le b &\equiv \neg(b < a) \\ a \ge b &\equiv \neg(a < b) \\ a == b &\equiv \neg(a < b)\ \wedge\ \neg(b < a) \\ a \ne b &\equiv \neg(a == b) \end{aligned}

Why this step? If neither a < b nor b < a is true, the two values cannot be ordered apart — so they must be equal. This is how a sort algorithm, knowing only <, can still tell things are equal.

Step 2 — each operator returns a Boolean, and Python Booleans are secretly integers:

$\texttt{True} = 1, \qquad \texttt{False} = 0$

Why this matters: True + True == 2 is valid Python. So sum(x > 0 for x in data) literally counts how many items are positive — comparisons become counters.

Worked examples

Worked example 1 — Numbers

print(7 == 7.0)   # True
print(7 != 8)     # True
print(3 <= 3)     # True
print(3 < 3)      # False

Why 7 == 7.0 is True? == compares value, not type. Python first widens int 7 to float 7.0, then checks equality.

Worked example 2 — Strings compare lexicographically (dictionary order)

print("apple" < "banana")  # True
print("Zebra" < "apple")   # True  (!)

Why "Zebra" < "apple"? Strings compare character by character using Unicode/ASCII code points. 'Z' is 90, 'a' is 97. Since 90 < 97, uppercase wins. Lesson: casing affects ordering — .lower() before comparing names.

Worked example 3 — Counting with comparisons

scores = [85, 40, 92, 55, 30]
passed = sum(s >= 50 for s in scores)   # 3

Why this step? Each s >= 50 is True(=1) or False(=0); sum adds the 1s. No if needed — comparisons are the counter.

Worked example 4 — Chaining for a range check

age = 25
if 18 <= age <= 60:
    print("eligible")

Why this step? Reads exactly like "18 ≤ age ≤ 60" and evaluates age once. Cleaner than age >= 18 and age <= 60.

Figure — Comparison operators — ==, !=, - , - , - =, - =

Common mistake Floating-point

== is a trap Why the wrong idea feels right: 0.1 + 0.2 should be 0.3, so 0.1 + 0.2 == 0.3 should be True. The truth: It's False. Binary can't store 0.1 exactly, so the sum is 0.30000000000000004. The fix: Compare with a tolerance:

abs((0.1 + 0.2) - 0.3) < 1e-9   # True

Common mistake

== vs is Why the wrong idea feels right: Both seem to mean "the same". The truth: == checks equal value; is checks same object in memory.

a = [1, 2]; b = [1, 2]
a == b   # True  (same contents)
a is b   # False (different objects)

The fix: Use == for values; reserve is for None (x is None).

Forecast-then-Verify

Recall Predict the output BEFORE reading on

print(5 > 3 > 1)
print("b" == "B")
print(True + (2 == 2))
print(1 == 1.0 == 1)

Answers: True (5>3 and 3>1) · False (case differs) · 2 (1 + True=1) · True (chained, all equal).

Active recall

What does a comparison operator always return?

A Boolean — True or False.

Difference between = and ==?

= assigns a value; == tests equality.

Why is 7 == 7.0 True?

== compares value, not type; int is widened to float.

What does a < b < c expand to in Python?

(a < b) and (b < c), with b evaluated once.

Why is 0.1 + 0.2 == 0.3 False?

Floating-point rounding; the sum is 0.30000000000000004.

How do you safely compare floats?

Check abs(x - y) < tiny_tolerance.

Difference between == and is?

== = equal value; is = same object identity.

What integer values do True and False equal?

True = 1, False = 0.

Why is "Zebra" < "apple" True?

Uppercase letters have smaller ASCII codes than lowercase.

How can sum(x > 0 for x in data) count positives?

Each comparison is 1 or 0; sum adds the 1s.

Recall Feynman: explain to a 12-year-old

Imagine a referee who only ever answers yes or no. You hand the referee two things and a question: "Is this bigger?" "Are these the same?" The referee never gives long answers — just a thumbs up (True) or thumbs down (False). Your program then does different things depending on the thumb. That's all a comparison operator is: a tiny yes/no referee. And here's a secret — thumbs up secretly counts as 1 and thumbs down as 0, so if you add up a bunch of thumbs-up you can count how many times "yes" happened!

Connections

Boolean values and type bool — the output type of every comparison
Logical operators — and, or, not — combine comparisons into bigger conditions
if-elif-else statements — comparisons drive every branch
while loops — loop condition is a comparison
Floating point representation — explains the == float trap
ASCII and Unicode — explains string ordering
Identity vs equality (is vs ==) — the deeper is/== story

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Comparison operators ek chhote referee jaise hote hain jo sirf haan ya naa bolte hain — yaani True ya False. Jab bhi tum do cheezon ke beech sawaal poochte ho ("kya yeh barabar hai?", "kya yeh bada hai?"), tab ==, !=, <, >, <=, >= ka use hota hai. Inka answer hamesha ek Boolean hota hai, aur yahi Boolean tumhare if aur while ko chalata hai.

Sabse common galti: = aur == ko mix kar dena. Yaad rakho — ek = value store karta hai (assignment), do == value check karta hai (test). "One equals sets, two equals tests." Agar tum if x = 5: likhoge to Python error de dega, jo actually achhi baat hai.

Ek mast trick: Python me True ka matlab 1 aur False ka matlab 0 hota hai. Isliye sum(s >= 50 for s in scores) seedha count kar deta hai ki kitne students pass hue — bina kisi if ke! Aur Python me chaining allowed hai: 18 <= age <= 60 bilkul maths ki tarah likh sakte ho, aur Python ise (18 <= age) and (age <= 60) me khol deta hai.

Ek warning: floats ke saath == mat karo. 0.1 + 0.2 == 0.3 actually False hota hai kyunki computer binary me exact 0.1 store nahi kar paata. Iske liye abs(a - b) < 1e-9 jaise tolerance check use karo. Yeh chhoti chhoti baatein hi tumhe ek strong programmer banati hain.

Test yourself — Introduction to Programming (Python)

Connections