TinyProf's Grammar Breakdown 🎓

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1. What We're Solving

We need to figure out whether "That" or "It" is the more appropriate pronoun when referring back to a mathematical formula or statement in formal academic writing. Was the copyeditor's change actually an improvement?

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2. The Approach

To solve this, we need to understand what these two pronouns do differently. They aren't always interchangeable! The key question is: what exactly is being referred to, and how specific is that reference?

Think of it this way — pronouns are like pointers. Some pointers are precise and deliberate; others are more casual and vague.

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3. Step-by-Step Solution

Step 1: Understand the Difference Between "That" and "It" as Pronouns

| Pronoun | What it does | |--------|-------------| | It | Refers to something as a continuous, ongoing topic — something already fully "in play" | | That | Calls attention to something specific and somewhat distances the speaker from it — almost saying "the thing I just showed you" |

> 💡 "That" has a slightly demonstrative quality. It points a finger. "It" is more like a casual handoff.

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Step 2: Look at the Original Sentence in Context

The sentence before says:

> "...the tangent of the sum of several angles is given by [expression]."

Then the next sentence begins referring to that formula/claim. Ask yourself:

• Has this formula been a long-running topic, casually referred to multiple times? No.
• Is the writer specifically pointing back to something just introduced? Yes!

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Step 3: Apply the "Demonstrative vs. Casual" Test

"That is proved by easy induction..."

• Feels like the writer is deliberately pointing at the formula just displayed
• Creates a sense of: "Pause — notice what I just showed you. HERE is why it works."
• This is common in mathematical and philosophical writing, where precision of reference matters enormously

"It is proved by easy induction..."

• Feels more like the formula was already an assumed, established topic
• Slightly more casual — almost as if the formula had been discussed for pages already
• Could also, in some readings, refer more loosely to the concept rather than the specific statement

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Step 4: Consider the Register (Formal Academic/Mathematical Writing)

In mathematics and formal academic prose, writers often use "that" as a demonstrative pronoun intentionally to:

• Signal a precise, bounded reference ("this specific thing, not a general idea")
• Create logical clarity — vital in proofs where ambiguity is dangerous
• Follow a long tradition in mathematical exposition

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Step 5: Was the Copyeditor Right?

Both are grammatically acceptable, but they carry different nuances:

• The copyeditor's "It" is not wrong, but it may have weakened the precision of the reference
• The original "That" was likely a deliberate stylistic and logical choice, especially fitting for a mathematical proof
• In this context, "That" is arguably the stronger and more appropriate choice

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4. The Answer

✅ The writer was right to question the change.

"That" is the more appropriate pronoun here because:

• 1. It demonstratively points to the specific formula just introduced
• 2. It creates precise logical reference — essential in mathematical writing
• 3. It follows established conventions in formal mathematical prose
• 4. The copyeditor's "It" isn't grammatically wrong, but it subtly dilutes the intentional precision of the original

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5. Memory Tip 💡

> "THAT points; IT floats." > > Use "that" when you want to specifically point a finger at something just mentioned. Use "it" when the topic has been floating around for a while and everyone already knows what you mean.

In formal writing — especially math and logic — when in doubt, be the pointer, not the floater! 🎯

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You're asking exactly the right kind of question by noticing these subtle distinctions. That critical attention to language is what separates good writers from great ones! 🌟