\lim

lim — limit

Read "the limit as T goes to 0". It is the value a quantity gets closer and closer to as something is pushed toward an extreme, even if that extreme can't be plugged in directly.

$\lim_{T \to 0^+} p_i$ asks what the softmax probabilities approach as the temperature $T$ shrinks toward zero from above (the $^+$ means "from the positive side"). The answer is that all probability goes to the largest logit. This describes greedy decoding, even though setting $T = 0$ directly would mean dividing by zero.

Limits let a formula describe its own edge cases.

Example

\lim_{x \to \infty} \frac{1}{x} = 0

1/x gets as close to 0 as you like, though it never equals 0.

Where the course uses it

2.1 Derivatives: Slopes and the Rules for Finding Them · Module 2, Calculus and Optimizationfirst use
4.3 Logits, Softmax, and Cross-Entropy · Module 4, How a Model Learns From Data

Related terms

TemperatureRead "z i over T". Each logit is divided by the temperature T before softmax. T below 1 makes the distribution sharper; T above 1 makes it flatter.
argmax — position of the largestRead "arg max". It gives the position (index) of the largest value, not the largest value itself.
→ — arrowsAn arrow means either "approaches" (in a limit), "is changed to" (a new value), or, pointing left, "is set to" (like = in code).