deepseek-ai

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DeepSeek-R1

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DeepSeek 41.2k

can you solve this problem?

It is used to force the model to "think" by making the first token == <think>

can you solve this problem?

one solution is to simply add <think> to the head of the response in your code.

This seems confusing, the output content is always missing the <think> start tag, and the reasoning_content of vllm will become null because it does not have the <think> tag.

can you solve this problem?

one solution is to simply add <think> to the head of the response in your code.

add <think> to the head of response?

messages = {"role":"user","content":"<think>"+text}]

is this right?

This seems confusing, the output content is always missing the <think> start tag, and the reasoning_content of vllm will become null because it does not have the <think> tag.

Can you show your result?

messages = {"role":"user","content":"<think> why 1+1 is 2?"}]

the result is 
output="""<think>\nOkay, the user is asking why 1 + 1 equals 2. Let me think about how to approach this.\n\nFirst, I should consider their background. They might not have a deep math understanding, so I need to explain it in simple terms. Maybe start with basic arithmetic principles.\n\nI recall that in Peano axioms, numbers are defined incrementally. So 1 is S(0), and 2 is S(S(0)). Adding 1 + 1 would be S(0) + S(0) = S(S(0)) which is 2. But that\'s probably too technical for a general audience.\n\nAlternatively, use the concept of counting objects. If you have one apple and add another, you have two. That\'s an intuitive example. But maybe they want a more formal answer.\n\nAlso, there\'s the definition of addition in set theory, where cardinalities combine. But again, that\'s more advanced. Should I mention different number systems? Like in binary, 1 + 1 is 10, but that\'s not relevant here since they\'re asking about base 10.\n\nPerhaps explain that \'2\' is just the symbol we assign to the successor of 1, and addition is defined such that adding 1 to any number gives its successor. So by definition, 1 + 1 is the next number, which is 2.\n\nWait, the user might be looking for a foundational proof. Maybe reference the Peano axioms or Principia Mathematica, where it takes many pages to prove 1+1=2. But that\'s probably too much detail. Need to balance simplicity and accuracy.\n\nAlso, consider if there\'s a cultural or linguistic angle. In some contexts, 1+1 could metaphorically not equal 2, but mathematically it\'s standard. The user is likely seeking a mathematical explanation.\n\nI should structure the answer starting with the intuitive example, then touch on the axiomatic approach without getting too deep, and maybe mention that in formal systems it\'s proven based on definitions. Make sure to keep it clear and not overwhelm them with jargon.\n</think>\n\nThe equation **1 + 1 = 2** is fundamental to arithmetic, but its "proof" depends on how deeply you want to explore the foundations of mathematics. Here’s a breakdown:\n\n### 1. **Intuitive Explanation**  \nIn everyday life, if you have **one object** (like an apple) and add **another**, you end up with **two objects**. This matches our physical experience of combining quantities. We use symbols (1, 2, +, =) to represent these concepts abstractly.\n\n---\n\n### 2. **Axiomatic Foundations**  \nFormally, mathematicians define numbers and operations using systems like **Peano axioms** or **set theory**:\n   - **Peano Axioms**: \n     - Start with a base number (**0**). \n     - Define the **successor function** $S(n)S(n)$, which gives the next number (e.g., $S(0)=1S(0)\; =\; 1$, $S(1)=2S(1)\; =\; 2$).\n     - Addition is defined recursively:\n       - $n+0=nn\; +\; 0\; =\; n$\n       - $n+S(m)=S(n+m)n\; +\; S(m)\; =\; S(n\; +\; m)$\n     - Applying this:  \n       $1+1=1+S(0)=S(1+0)=S(1)=21\; +\; 1\; =\; 1\; +\; S(0)\; =\; S(1\; +\; 0)\; =\; S(1)\; =\; 2$.\n\n   - **Set Theory** (e.g., Zermelo-Fraenkel):  \n     Numbers are constructed from sets. For example:\n     - $0=0\; =\; \backslash \backslash \{\backslash \backslash \}$ (empty set),\n     - $1=01\; =\; \backslash \backslash \{0\backslash \backslash \}$,\n     - $2=0,12\; =\; \backslash \backslash \{0,\; 1\backslash \backslash \}$.\n     - Addition is defined via unions and successors.\n\n---\n\n### 3. **Why Does It Feel Obvious?**  \nWe’re taught this as a basic truth because it aligns with both logic and our physical world. However, in formal systems, proving $1+1=21\; +\; 1\; =\; 2$ requires rigorously defining **numbers**, **addition**, and **equality**. For instance, in Whitehead and Russell’s *Principia Mathematica*, it takes hundreds of pages to establish this result!\n\n---\n\n### 4. **Is It Always True?**  \n- In standard arithmetic: **Yes** (by definition).  \n- In modular arithmetic (e.g., modulo 2): $1+1=01\; +\; 1\; =\; 0$.  \n- Metaphorically: Sometimes "1 + 1 > 2" (synergy) or "1 + 1 < 2" (inefficiency), but these aren’t mathematical claims.\n\n---\n\nIn summary, **1 + 1 = 2** is true by the definitions and axioms we use to construct arithmetic. Its simplicity masks deep foundations, but for practical purposes, it’s a cornerstone of logic and mathematics. 🧮"""